2 * Copyright 2010 INRIA Saclay
4 * Use of this software is governed by the MIT license
6 * Written by Sven Verdoolaege, INRIA Saclay - Ile-de-France,
7 * Parc Club Orsay Universite, ZAC des vignes, 4 rue Jacques Monod,
13 #include <isl_ctx_private.h>
14 #include <isl_map_private.h>
15 #include <isl_factorization.h>
16 #include <isl_lp_private.h>
18 #include <isl_union_map_private.h>
19 #include <isl_constraint_private.h>
20 #include <isl_polynomial_private.h>
21 #include <isl_point_private.h>
22 #include <isl_space_private.h>
23 #include <isl_mat_private.h>
24 #include <isl_vec_private.h>
25 #include <isl_range.h>
26 #include <isl_local_space_private.h>
27 #include <isl_aff_private.h>
28 #include <isl_val_private.h>
29 #include <isl_config.h>
30 #include <isl/deprecated/polynomial_int.h>
32 static unsigned pos(__isl_keep isl_space
*dim
, enum isl_dim_type type
)
35 case isl_dim_param
: return 0;
36 case isl_dim_in
: return dim
->nparam
;
37 case isl_dim_out
: return dim
->nparam
+ dim
->n_in
;
42 int isl_upoly_is_cst(__isl_keep
struct isl_upoly
*up
)
50 __isl_keep
struct isl_upoly_cst
*isl_upoly_as_cst(__isl_keep
struct isl_upoly
*up
)
55 isl_assert(up
->ctx
, up
->var
< 0, return NULL
);
57 return (struct isl_upoly_cst
*)up
;
60 __isl_keep
struct isl_upoly_rec
*isl_upoly_as_rec(__isl_keep
struct isl_upoly
*up
)
65 isl_assert(up
->ctx
, up
->var
>= 0, return NULL
);
67 return (struct isl_upoly_rec
*)up
;
70 int isl_upoly_is_equal(__isl_keep
struct isl_upoly
*up1
,
71 __isl_keep
struct isl_upoly
*up2
)
74 struct isl_upoly_rec
*rec1
, *rec2
;
80 if (up1
->var
!= up2
->var
)
82 if (isl_upoly_is_cst(up1
)) {
83 struct isl_upoly_cst
*cst1
, *cst2
;
84 cst1
= isl_upoly_as_cst(up1
);
85 cst2
= isl_upoly_as_cst(up2
);
88 return isl_int_eq(cst1
->n
, cst2
->n
) &&
89 isl_int_eq(cst1
->d
, cst2
->d
);
92 rec1
= isl_upoly_as_rec(up1
);
93 rec2
= isl_upoly_as_rec(up2
);
97 if (rec1
->n
!= rec2
->n
)
100 for (i
= 0; i
< rec1
->n
; ++i
) {
101 int eq
= isl_upoly_is_equal(rec1
->p
[i
], rec2
->p
[i
]);
109 int isl_upoly_is_zero(__isl_keep
struct isl_upoly
*up
)
111 struct isl_upoly_cst
*cst
;
115 if (!isl_upoly_is_cst(up
))
118 cst
= isl_upoly_as_cst(up
);
122 return isl_int_is_zero(cst
->n
) && isl_int_is_pos(cst
->d
);
125 int isl_upoly_sgn(__isl_keep
struct isl_upoly
*up
)
127 struct isl_upoly_cst
*cst
;
131 if (!isl_upoly_is_cst(up
))
134 cst
= isl_upoly_as_cst(up
);
138 return isl_int_sgn(cst
->n
);
141 int isl_upoly_is_nan(__isl_keep
struct isl_upoly
*up
)
143 struct isl_upoly_cst
*cst
;
147 if (!isl_upoly_is_cst(up
))
150 cst
= isl_upoly_as_cst(up
);
154 return isl_int_is_zero(cst
->n
) && isl_int_is_zero(cst
->d
);
157 int isl_upoly_is_infty(__isl_keep
struct isl_upoly
*up
)
159 struct isl_upoly_cst
*cst
;
163 if (!isl_upoly_is_cst(up
))
166 cst
= isl_upoly_as_cst(up
);
170 return isl_int_is_pos(cst
->n
) && isl_int_is_zero(cst
->d
);
173 int isl_upoly_is_neginfty(__isl_keep
struct isl_upoly
*up
)
175 struct isl_upoly_cst
*cst
;
179 if (!isl_upoly_is_cst(up
))
182 cst
= isl_upoly_as_cst(up
);
186 return isl_int_is_neg(cst
->n
) && isl_int_is_zero(cst
->d
);
189 int isl_upoly_is_one(__isl_keep
struct isl_upoly
*up
)
191 struct isl_upoly_cst
*cst
;
195 if (!isl_upoly_is_cst(up
))
198 cst
= isl_upoly_as_cst(up
);
202 return isl_int_eq(cst
->n
, cst
->d
) && isl_int_is_pos(cst
->d
);
205 int isl_upoly_is_negone(__isl_keep
struct isl_upoly
*up
)
207 struct isl_upoly_cst
*cst
;
211 if (!isl_upoly_is_cst(up
))
214 cst
= isl_upoly_as_cst(up
);
218 return isl_int_is_negone(cst
->n
) && isl_int_is_one(cst
->d
);
221 __isl_give
struct isl_upoly_cst
*isl_upoly_cst_alloc(struct isl_ctx
*ctx
)
223 struct isl_upoly_cst
*cst
;
225 cst
= isl_alloc_type(ctx
, struct isl_upoly_cst
);
234 isl_int_init(cst
->n
);
235 isl_int_init(cst
->d
);
240 __isl_give
struct isl_upoly
*isl_upoly_zero(struct isl_ctx
*ctx
)
242 struct isl_upoly_cst
*cst
;
244 cst
= isl_upoly_cst_alloc(ctx
);
248 isl_int_set_si(cst
->n
, 0);
249 isl_int_set_si(cst
->d
, 1);
254 __isl_give
struct isl_upoly
*isl_upoly_one(struct isl_ctx
*ctx
)
256 struct isl_upoly_cst
*cst
;
258 cst
= isl_upoly_cst_alloc(ctx
);
262 isl_int_set_si(cst
->n
, 1);
263 isl_int_set_si(cst
->d
, 1);
268 __isl_give
struct isl_upoly
*isl_upoly_infty(struct isl_ctx
*ctx
)
270 struct isl_upoly_cst
*cst
;
272 cst
= isl_upoly_cst_alloc(ctx
);
276 isl_int_set_si(cst
->n
, 1);
277 isl_int_set_si(cst
->d
, 0);
282 __isl_give
struct isl_upoly
*isl_upoly_neginfty(struct isl_ctx
*ctx
)
284 struct isl_upoly_cst
*cst
;
286 cst
= isl_upoly_cst_alloc(ctx
);
290 isl_int_set_si(cst
->n
, -1);
291 isl_int_set_si(cst
->d
, 0);
296 __isl_give
struct isl_upoly
*isl_upoly_nan(struct isl_ctx
*ctx
)
298 struct isl_upoly_cst
*cst
;
300 cst
= isl_upoly_cst_alloc(ctx
);
304 isl_int_set_si(cst
->n
, 0);
305 isl_int_set_si(cst
->d
, 0);
310 __isl_give
struct isl_upoly
*isl_upoly_rat_cst(struct isl_ctx
*ctx
,
311 isl_int n
, isl_int d
)
313 struct isl_upoly_cst
*cst
;
315 cst
= isl_upoly_cst_alloc(ctx
);
319 isl_int_set(cst
->n
, n
);
320 isl_int_set(cst
->d
, d
);
325 __isl_give
struct isl_upoly_rec
*isl_upoly_alloc_rec(struct isl_ctx
*ctx
,
328 struct isl_upoly_rec
*rec
;
330 isl_assert(ctx
, var
>= 0, return NULL
);
331 isl_assert(ctx
, size
>= 0, return NULL
);
332 rec
= isl_calloc(ctx
, struct isl_upoly_rec
,
333 sizeof(struct isl_upoly_rec
) +
334 size
* sizeof(struct isl_upoly
*));
349 __isl_give isl_qpolynomial
*isl_qpolynomial_reset_domain_space(
350 __isl_take isl_qpolynomial
*qp
, __isl_take isl_space
*dim
)
352 qp
= isl_qpolynomial_cow(qp
);
356 isl_space_free(qp
->dim
);
361 isl_qpolynomial_free(qp
);
366 /* Reset the space of "qp". This function is called from isl_pw_templ.c
367 * and doesn't know if the space of an element object is represented
368 * directly or through its domain. It therefore passes along both.
370 __isl_give isl_qpolynomial
*isl_qpolynomial_reset_space_and_domain(
371 __isl_take isl_qpolynomial
*qp
, __isl_take isl_space
*space
,
372 __isl_take isl_space
*domain
)
374 isl_space_free(space
);
375 return isl_qpolynomial_reset_domain_space(qp
, domain
);
378 isl_ctx
*isl_qpolynomial_get_ctx(__isl_keep isl_qpolynomial
*qp
)
380 return qp
? qp
->dim
->ctx
: NULL
;
383 __isl_give isl_space
*isl_qpolynomial_get_domain_space(
384 __isl_keep isl_qpolynomial
*qp
)
386 return qp
? isl_space_copy(qp
->dim
) : NULL
;
389 __isl_give isl_space
*isl_qpolynomial_get_space(__isl_keep isl_qpolynomial
*qp
)
394 space
= isl_space_copy(qp
->dim
);
395 space
= isl_space_from_domain(space
);
396 space
= isl_space_add_dims(space
, isl_dim_out
, 1);
400 /* Externally, an isl_qpolynomial has a map space, but internally, the
401 * ls field corresponds to the domain of that space.
403 unsigned isl_qpolynomial_dim(__isl_keep isl_qpolynomial
*qp
,
404 enum isl_dim_type type
)
408 if (type
== isl_dim_out
)
410 if (type
== isl_dim_in
)
412 return isl_space_dim(qp
->dim
, type
);
415 int isl_qpolynomial_is_zero(__isl_keep isl_qpolynomial
*qp
)
417 return qp
? isl_upoly_is_zero(qp
->upoly
) : -1;
420 int isl_qpolynomial_is_one(__isl_keep isl_qpolynomial
*qp
)
422 return qp
? isl_upoly_is_one(qp
->upoly
) : -1;
425 int isl_qpolynomial_is_nan(__isl_keep isl_qpolynomial
*qp
)
427 return qp
? isl_upoly_is_nan(qp
->upoly
) : -1;
430 int isl_qpolynomial_is_infty(__isl_keep isl_qpolynomial
*qp
)
432 return qp
? isl_upoly_is_infty(qp
->upoly
) : -1;
435 int isl_qpolynomial_is_neginfty(__isl_keep isl_qpolynomial
*qp
)
437 return qp
? isl_upoly_is_neginfty(qp
->upoly
) : -1;
440 int isl_qpolynomial_sgn(__isl_keep isl_qpolynomial
*qp
)
442 return qp
? isl_upoly_sgn(qp
->upoly
) : 0;
445 static void upoly_free_cst(__isl_take
struct isl_upoly_cst
*cst
)
447 isl_int_clear(cst
->n
);
448 isl_int_clear(cst
->d
);
451 static void upoly_free_rec(__isl_take
struct isl_upoly_rec
*rec
)
455 for (i
= 0; i
< rec
->n
; ++i
)
456 isl_upoly_free(rec
->p
[i
]);
459 __isl_give
struct isl_upoly
*isl_upoly_copy(__isl_keep
struct isl_upoly
*up
)
468 __isl_give
struct isl_upoly
*isl_upoly_dup_cst(__isl_keep
struct isl_upoly
*up
)
470 struct isl_upoly_cst
*cst
;
471 struct isl_upoly_cst
*dup
;
473 cst
= isl_upoly_as_cst(up
);
477 dup
= isl_upoly_as_cst(isl_upoly_zero(up
->ctx
));
480 isl_int_set(dup
->n
, cst
->n
);
481 isl_int_set(dup
->d
, cst
->d
);
486 __isl_give
struct isl_upoly
*isl_upoly_dup_rec(__isl_keep
struct isl_upoly
*up
)
489 struct isl_upoly_rec
*rec
;
490 struct isl_upoly_rec
*dup
;
492 rec
= isl_upoly_as_rec(up
);
496 dup
= isl_upoly_alloc_rec(up
->ctx
, up
->var
, rec
->n
);
500 for (i
= 0; i
< rec
->n
; ++i
) {
501 dup
->p
[i
] = isl_upoly_copy(rec
->p
[i
]);
509 isl_upoly_free(&dup
->up
);
513 __isl_give
struct isl_upoly
*isl_upoly_dup(__isl_keep
struct isl_upoly
*up
)
518 if (isl_upoly_is_cst(up
))
519 return isl_upoly_dup_cst(up
);
521 return isl_upoly_dup_rec(up
);
524 __isl_give
struct isl_upoly
*isl_upoly_cow(__isl_take
struct isl_upoly
*up
)
532 return isl_upoly_dup(up
);
535 void isl_upoly_free(__isl_take
struct isl_upoly
*up
)
544 upoly_free_cst((struct isl_upoly_cst
*)up
);
546 upoly_free_rec((struct isl_upoly_rec
*)up
);
548 isl_ctx_deref(up
->ctx
);
552 static void isl_upoly_cst_reduce(__isl_keep
struct isl_upoly_cst
*cst
)
557 isl_int_gcd(gcd
, cst
->n
, cst
->d
);
558 if (!isl_int_is_zero(gcd
) && !isl_int_is_one(gcd
)) {
559 isl_int_divexact(cst
->n
, cst
->n
, gcd
);
560 isl_int_divexact(cst
->d
, cst
->d
, gcd
);
565 __isl_give
struct isl_upoly
*isl_upoly_sum_cst(__isl_take
struct isl_upoly
*up1
,
566 __isl_take
struct isl_upoly
*up2
)
568 struct isl_upoly_cst
*cst1
;
569 struct isl_upoly_cst
*cst2
;
571 up1
= isl_upoly_cow(up1
);
575 cst1
= isl_upoly_as_cst(up1
);
576 cst2
= isl_upoly_as_cst(up2
);
578 if (isl_int_eq(cst1
->d
, cst2
->d
))
579 isl_int_add(cst1
->n
, cst1
->n
, cst2
->n
);
581 isl_int_mul(cst1
->n
, cst1
->n
, cst2
->d
);
582 isl_int_addmul(cst1
->n
, cst2
->n
, cst1
->d
);
583 isl_int_mul(cst1
->d
, cst1
->d
, cst2
->d
);
586 isl_upoly_cst_reduce(cst1
);
596 static __isl_give
struct isl_upoly
*replace_by_zero(
597 __isl_take
struct isl_upoly
*up
)
605 return isl_upoly_zero(ctx
);
608 static __isl_give
struct isl_upoly
*replace_by_constant_term(
609 __isl_take
struct isl_upoly
*up
)
611 struct isl_upoly_rec
*rec
;
612 struct isl_upoly
*cst
;
617 rec
= isl_upoly_as_rec(up
);
620 cst
= isl_upoly_copy(rec
->p
[0]);
628 __isl_give
struct isl_upoly
*isl_upoly_sum(__isl_take
struct isl_upoly
*up1
,
629 __isl_take
struct isl_upoly
*up2
)
632 struct isl_upoly_rec
*rec1
, *rec2
;
637 if (isl_upoly_is_nan(up1
)) {
642 if (isl_upoly_is_nan(up2
)) {
647 if (isl_upoly_is_zero(up1
)) {
652 if (isl_upoly_is_zero(up2
)) {
657 if (up1
->var
< up2
->var
)
658 return isl_upoly_sum(up2
, up1
);
660 if (up2
->var
< up1
->var
) {
661 struct isl_upoly_rec
*rec
;
662 if (isl_upoly_is_infty(up2
) || isl_upoly_is_neginfty(up2
)) {
666 up1
= isl_upoly_cow(up1
);
667 rec
= isl_upoly_as_rec(up1
);
670 rec
->p
[0] = isl_upoly_sum(rec
->p
[0], up2
);
672 up1
= replace_by_constant_term(up1
);
676 if (isl_upoly_is_cst(up1
))
677 return isl_upoly_sum_cst(up1
, up2
);
679 rec1
= isl_upoly_as_rec(up1
);
680 rec2
= isl_upoly_as_rec(up2
);
684 if (rec1
->n
< rec2
->n
)
685 return isl_upoly_sum(up2
, up1
);
687 up1
= isl_upoly_cow(up1
);
688 rec1
= isl_upoly_as_rec(up1
);
692 for (i
= rec2
->n
- 1; i
>= 0; --i
) {
693 rec1
->p
[i
] = isl_upoly_sum(rec1
->p
[i
],
694 isl_upoly_copy(rec2
->p
[i
]));
697 if (i
== rec1
->n
- 1 && isl_upoly_is_zero(rec1
->p
[i
])) {
698 isl_upoly_free(rec1
->p
[i
]);
704 up1
= replace_by_zero(up1
);
705 else if (rec1
->n
== 1)
706 up1
= replace_by_constant_term(up1
);
717 __isl_give
struct isl_upoly
*isl_upoly_cst_add_isl_int(
718 __isl_take
struct isl_upoly
*up
, isl_int v
)
720 struct isl_upoly_cst
*cst
;
722 up
= isl_upoly_cow(up
);
726 cst
= isl_upoly_as_cst(up
);
728 isl_int_addmul(cst
->n
, cst
->d
, v
);
733 __isl_give
struct isl_upoly
*isl_upoly_add_isl_int(
734 __isl_take
struct isl_upoly
*up
, isl_int v
)
736 struct isl_upoly_rec
*rec
;
741 if (isl_upoly_is_cst(up
))
742 return isl_upoly_cst_add_isl_int(up
, v
);
744 up
= isl_upoly_cow(up
);
745 rec
= isl_upoly_as_rec(up
);
749 rec
->p
[0] = isl_upoly_add_isl_int(rec
->p
[0], v
);
759 __isl_give
struct isl_upoly
*isl_upoly_cst_mul_isl_int(
760 __isl_take
struct isl_upoly
*up
, isl_int v
)
762 struct isl_upoly_cst
*cst
;
764 if (isl_upoly_is_zero(up
))
767 up
= isl_upoly_cow(up
);
771 cst
= isl_upoly_as_cst(up
);
773 isl_int_mul(cst
->n
, cst
->n
, v
);
778 __isl_give
struct isl_upoly
*isl_upoly_mul_isl_int(
779 __isl_take
struct isl_upoly
*up
, isl_int v
)
782 struct isl_upoly_rec
*rec
;
787 if (isl_upoly_is_cst(up
))
788 return isl_upoly_cst_mul_isl_int(up
, v
);
790 up
= isl_upoly_cow(up
);
791 rec
= isl_upoly_as_rec(up
);
795 for (i
= 0; i
< rec
->n
; ++i
) {
796 rec
->p
[i
] = isl_upoly_mul_isl_int(rec
->p
[i
], v
);
807 /* Multiply the constant polynomial "up" by "v".
809 static __isl_give
struct isl_upoly
*isl_upoly_cst_scale_val(
810 __isl_take
struct isl_upoly
*up
, __isl_keep isl_val
*v
)
812 struct isl_upoly_cst
*cst
;
814 if (isl_upoly_is_zero(up
))
817 up
= isl_upoly_cow(up
);
821 cst
= isl_upoly_as_cst(up
);
823 isl_int_mul(cst
->n
, cst
->n
, v
->n
);
824 isl_int_mul(cst
->d
, cst
->d
, v
->d
);
825 isl_upoly_cst_reduce(cst
);
830 /* Multiply the polynomial "up" by "v".
832 static __isl_give
struct isl_upoly
*isl_upoly_scale_val(
833 __isl_take
struct isl_upoly
*up
, __isl_keep isl_val
*v
)
836 struct isl_upoly_rec
*rec
;
841 if (isl_upoly_is_cst(up
))
842 return isl_upoly_cst_scale_val(up
, v
);
844 up
= isl_upoly_cow(up
);
845 rec
= isl_upoly_as_rec(up
);
849 for (i
= 0; i
< rec
->n
; ++i
) {
850 rec
->p
[i
] = isl_upoly_scale_val(rec
->p
[i
], v
);
861 __isl_give
struct isl_upoly
*isl_upoly_mul_cst(__isl_take
struct isl_upoly
*up1
,
862 __isl_take
struct isl_upoly
*up2
)
864 struct isl_upoly_cst
*cst1
;
865 struct isl_upoly_cst
*cst2
;
867 up1
= isl_upoly_cow(up1
);
871 cst1
= isl_upoly_as_cst(up1
);
872 cst2
= isl_upoly_as_cst(up2
);
874 isl_int_mul(cst1
->n
, cst1
->n
, cst2
->n
);
875 isl_int_mul(cst1
->d
, cst1
->d
, cst2
->d
);
877 isl_upoly_cst_reduce(cst1
);
887 __isl_give
struct isl_upoly
*isl_upoly_mul_rec(__isl_take
struct isl_upoly
*up1
,
888 __isl_take
struct isl_upoly
*up2
)
890 struct isl_upoly_rec
*rec1
;
891 struct isl_upoly_rec
*rec2
;
892 struct isl_upoly_rec
*res
= NULL
;
896 rec1
= isl_upoly_as_rec(up1
);
897 rec2
= isl_upoly_as_rec(up2
);
900 size
= rec1
->n
+ rec2
->n
- 1;
901 res
= isl_upoly_alloc_rec(up1
->ctx
, up1
->var
, size
);
905 for (i
= 0; i
< rec1
->n
; ++i
) {
906 res
->p
[i
] = isl_upoly_mul(isl_upoly_copy(rec2
->p
[0]),
907 isl_upoly_copy(rec1
->p
[i
]));
912 for (; i
< size
; ++i
) {
913 res
->p
[i
] = isl_upoly_zero(up1
->ctx
);
918 for (i
= 0; i
< rec1
->n
; ++i
) {
919 for (j
= 1; j
< rec2
->n
; ++j
) {
920 struct isl_upoly
*up
;
921 up
= isl_upoly_mul(isl_upoly_copy(rec2
->p
[j
]),
922 isl_upoly_copy(rec1
->p
[i
]));
923 res
->p
[i
+ j
] = isl_upoly_sum(res
->p
[i
+ j
], up
);
936 isl_upoly_free(&res
->up
);
940 __isl_give
struct isl_upoly
*isl_upoly_mul(__isl_take
struct isl_upoly
*up1
,
941 __isl_take
struct isl_upoly
*up2
)
946 if (isl_upoly_is_nan(up1
)) {
951 if (isl_upoly_is_nan(up2
)) {
956 if (isl_upoly_is_zero(up1
)) {
961 if (isl_upoly_is_zero(up2
)) {
966 if (isl_upoly_is_one(up1
)) {
971 if (isl_upoly_is_one(up2
)) {
976 if (up1
->var
< up2
->var
)
977 return isl_upoly_mul(up2
, up1
);
979 if (up2
->var
< up1
->var
) {
981 struct isl_upoly_rec
*rec
;
982 if (isl_upoly_is_infty(up2
) || isl_upoly_is_neginfty(up2
)) {
983 isl_ctx
*ctx
= up1
->ctx
;
986 return isl_upoly_nan(ctx
);
988 up1
= isl_upoly_cow(up1
);
989 rec
= isl_upoly_as_rec(up1
);
993 for (i
= 0; i
< rec
->n
; ++i
) {
994 rec
->p
[i
] = isl_upoly_mul(rec
->p
[i
],
995 isl_upoly_copy(up2
));
1003 if (isl_upoly_is_cst(up1
))
1004 return isl_upoly_mul_cst(up1
, up2
);
1006 return isl_upoly_mul_rec(up1
, up2
);
1008 isl_upoly_free(up1
);
1009 isl_upoly_free(up2
);
1013 __isl_give
struct isl_upoly
*isl_upoly_pow(__isl_take
struct isl_upoly
*up
,
1016 struct isl_upoly
*res
;
1024 res
= isl_upoly_copy(up
);
1026 res
= isl_upoly_one(up
->ctx
);
1028 while (power
>>= 1) {
1029 up
= isl_upoly_mul(up
, isl_upoly_copy(up
));
1031 res
= isl_upoly_mul(res
, isl_upoly_copy(up
));
1038 __isl_give isl_qpolynomial
*isl_qpolynomial_alloc(__isl_take isl_space
*dim
,
1039 unsigned n_div
, __isl_take
struct isl_upoly
*up
)
1041 struct isl_qpolynomial
*qp
= NULL
;
1047 if (!isl_space_is_set(dim
))
1048 isl_die(isl_space_get_ctx(dim
), isl_error_invalid
,
1049 "domain of polynomial should be a set", goto error
);
1051 total
= isl_space_dim(dim
, isl_dim_all
);
1053 qp
= isl_calloc_type(dim
->ctx
, struct isl_qpolynomial
);
1058 qp
->div
= isl_mat_alloc(dim
->ctx
, n_div
, 1 + 1 + total
+ n_div
);
1067 isl_space_free(dim
);
1069 isl_qpolynomial_free(qp
);
1073 __isl_give isl_qpolynomial
*isl_qpolynomial_copy(__isl_keep isl_qpolynomial
*qp
)
1082 __isl_give isl_qpolynomial
*isl_qpolynomial_dup(__isl_keep isl_qpolynomial
*qp
)
1084 struct isl_qpolynomial
*dup
;
1089 dup
= isl_qpolynomial_alloc(isl_space_copy(qp
->dim
), qp
->div
->n_row
,
1090 isl_upoly_copy(qp
->upoly
));
1093 isl_mat_free(dup
->div
);
1094 dup
->div
= isl_mat_copy(qp
->div
);
1100 isl_qpolynomial_free(dup
);
1104 __isl_give isl_qpolynomial
*isl_qpolynomial_cow(__isl_take isl_qpolynomial
*qp
)
1112 return isl_qpolynomial_dup(qp
);
1115 void *isl_qpolynomial_free(__isl_take isl_qpolynomial
*qp
)
1123 isl_space_free(qp
->dim
);
1124 isl_mat_free(qp
->div
);
1125 isl_upoly_free(qp
->upoly
);
1131 __isl_give
struct isl_upoly
*isl_upoly_var_pow(isl_ctx
*ctx
, int pos
, int power
)
1134 struct isl_upoly_rec
*rec
;
1135 struct isl_upoly_cst
*cst
;
1137 rec
= isl_upoly_alloc_rec(ctx
, pos
, 1 + power
);
1140 for (i
= 0; i
< 1 + power
; ++i
) {
1141 rec
->p
[i
] = isl_upoly_zero(ctx
);
1146 cst
= isl_upoly_as_cst(rec
->p
[power
]);
1147 isl_int_set_si(cst
->n
, 1);
1151 isl_upoly_free(&rec
->up
);
1155 /* r array maps original positions to new positions.
1157 static __isl_give
struct isl_upoly
*reorder(__isl_take
struct isl_upoly
*up
,
1161 struct isl_upoly_rec
*rec
;
1162 struct isl_upoly
*base
;
1163 struct isl_upoly
*res
;
1165 if (isl_upoly_is_cst(up
))
1168 rec
= isl_upoly_as_rec(up
);
1172 isl_assert(up
->ctx
, rec
->n
>= 1, goto error
);
1174 base
= isl_upoly_var_pow(up
->ctx
, r
[up
->var
], 1);
1175 res
= reorder(isl_upoly_copy(rec
->p
[rec
->n
- 1]), r
);
1177 for (i
= rec
->n
- 2; i
>= 0; --i
) {
1178 res
= isl_upoly_mul(res
, isl_upoly_copy(base
));
1179 res
= isl_upoly_sum(res
, reorder(isl_upoly_copy(rec
->p
[i
]), r
));
1182 isl_upoly_free(base
);
1191 static int compatible_divs(__isl_keep isl_mat
*div1
, __isl_keep isl_mat
*div2
)
1196 isl_assert(div1
->ctx
, div1
->n_row
>= div2
->n_row
&&
1197 div1
->n_col
>= div2
->n_col
, return -1);
1199 if (div1
->n_row
== div2
->n_row
)
1200 return isl_mat_is_equal(div1
, div2
);
1202 n_row
= div1
->n_row
;
1203 n_col
= div1
->n_col
;
1204 div1
->n_row
= div2
->n_row
;
1205 div1
->n_col
= div2
->n_col
;
1207 equal
= isl_mat_is_equal(div1
, div2
);
1209 div1
->n_row
= n_row
;
1210 div1
->n_col
= n_col
;
1215 static int cmp_row(__isl_keep isl_mat
*div
, int i
, int j
)
1219 li
= isl_seq_last_non_zero(div
->row
[i
], div
->n_col
);
1220 lj
= isl_seq_last_non_zero(div
->row
[j
], div
->n_col
);
1225 return isl_seq_cmp(div
->row
[i
], div
->row
[j
], div
->n_col
);
1228 struct isl_div_sort_info
{
1233 static int div_sort_cmp(const void *p1
, const void *p2
)
1235 const struct isl_div_sort_info
*i1
, *i2
;
1236 i1
= (const struct isl_div_sort_info
*) p1
;
1237 i2
= (const struct isl_div_sort_info
*) p2
;
1239 return cmp_row(i1
->div
, i1
->row
, i2
->row
);
1242 /* Sort divs and remove duplicates.
1244 static __isl_give isl_qpolynomial
*sort_divs(__isl_take isl_qpolynomial
*qp
)
1249 struct isl_div_sort_info
*array
= NULL
;
1250 int *pos
= NULL
, *at
= NULL
;
1251 int *reordering
= NULL
;
1256 if (qp
->div
->n_row
<= 1)
1259 div_pos
= isl_space_dim(qp
->dim
, isl_dim_all
);
1261 array
= isl_alloc_array(qp
->div
->ctx
, struct isl_div_sort_info
,
1263 pos
= isl_alloc_array(qp
->div
->ctx
, int, qp
->div
->n_row
);
1264 at
= isl_alloc_array(qp
->div
->ctx
, int, qp
->div
->n_row
);
1265 len
= qp
->div
->n_col
- 2;
1266 reordering
= isl_alloc_array(qp
->div
->ctx
, int, len
);
1267 if (!array
|| !pos
|| !at
|| !reordering
)
1270 for (i
= 0; i
< qp
->div
->n_row
; ++i
) {
1271 array
[i
].div
= qp
->div
;
1277 qsort(array
, qp
->div
->n_row
, sizeof(struct isl_div_sort_info
),
1280 for (i
= 0; i
< div_pos
; ++i
)
1283 for (i
= 0; i
< qp
->div
->n_row
; ++i
) {
1284 if (pos
[array
[i
].row
] == i
)
1286 qp
->div
= isl_mat_swap_rows(qp
->div
, i
, pos
[array
[i
].row
]);
1287 pos
[at
[i
]] = pos
[array
[i
].row
];
1288 at
[pos
[array
[i
].row
]] = at
[i
];
1289 at
[i
] = array
[i
].row
;
1290 pos
[array
[i
].row
] = i
;
1294 for (i
= 0; i
< len
- div_pos
; ++i
) {
1296 isl_seq_eq(qp
->div
->row
[i
- skip
- 1],
1297 qp
->div
->row
[i
- skip
], qp
->div
->n_col
)) {
1298 qp
->div
= isl_mat_drop_rows(qp
->div
, i
- skip
, 1);
1299 isl_mat_col_add(qp
->div
, 2 + div_pos
+ i
- skip
- 1,
1300 2 + div_pos
+ i
- skip
);
1301 qp
->div
= isl_mat_drop_cols(qp
->div
,
1302 2 + div_pos
+ i
- skip
, 1);
1305 reordering
[div_pos
+ array
[i
].row
] = div_pos
+ i
- skip
;
1308 qp
->upoly
= reorder(qp
->upoly
, reordering
);
1310 if (!qp
->upoly
|| !qp
->div
)
1324 isl_qpolynomial_free(qp
);
1328 static __isl_give
struct isl_upoly
*expand(__isl_take
struct isl_upoly
*up
,
1329 int *exp
, int first
)
1332 struct isl_upoly_rec
*rec
;
1334 if (isl_upoly_is_cst(up
))
1337 if (up
->var
< first
)
1340 if (exp
[up
->var
- first
] == up
->var
- first
)
1343 up
= isl_upoly_cow(up
);
1347 up
->var
= exp
[up
->var
- first
] + first
;
1349 rec
= isl_upoly_as_rec(up
);
1353 for (i
= 0; i
< rec
->n
; ++i
) {
1354 rec
->p
[i
] = expand(rec
->p
[i
], exp
, first
);
1365 static __isl_give isl_qpolynomial
*with_merged_divs(
1366 __isl_give isl_qpolynomial
*(*fn
)(__isl_take isl_qpolynomial
*qp1
,
1367 __isl_take isl_qpolynomial
*qp2
),
1368 __isl_take isl_qpolynomial
*qp1
, __isl_take isl_qpolynomial
*qp2
)
1372 isl_mat
*div
= NULL
;
1374 qp1
= isl_qpolynomial_cow(qp1
);
1375 qp2
= isl_qpolynomial_cow(qp2
);
1380 isl_assert(qp1
->div
->ctx
, qp1
->div
->n_row
>= qp2
->div
->n_row
&&
1381 qp1
->div
->n_col
>= qp2
->div
->n_col
, goto error
);
1383 exp1
= isl_alloc_array(qp1
->div
->ctx
, int, qp1
->div
->n_row
);
1384 exp2
= isl_alloc_array(qp2
->div
->ctx
, int, qp2
->div
->n_row
);
1388 div
= isl_merge_divs(qp1
->div
, qp2
->div
, exp1
, exp2
);
1392 isl_mat_free(qp1
->div
);
1393 qp1
->div
= isl_mat_copy(div
);
1394 isl_mat_free(qp2
->div
);
1395 qp2
->div
= isl_mat_copy(div
);
1397 qp1
->upoly
= expand(qp1
->upoly
, exp1
, div
->n_col
- div
->n_row
- 2);
1398 qp2
->upoly
= expand(qp2
->upoly
, exp2
, div
->n_col
- div
->n_row
- 2);
1400 if (!qp1
->upoly
|| !qp2
->upoly
)
1407 return fn(qp1
, qp2
);
1412 isl_qpolynomial_free(qp1
);
1413 isl_qpolynomial_free(qp2
);
1417 __isl_give isl_qpolynomial
*isl_qpolynomial_add(__isl_take isl_qpolynomial
*qp1
,
1418 __isl_take isl_qpolynomial
*qp2
)
1420 qp1
= isl_qpolynomial_cow(qp1
);
1425 if (qp1
->div
->n_row
< qp2
->div
->n_row
)
1426 return isl_qpolynomial_add(qp2
, qp1
);
1428 isl_assert(qp1
->dim
->ctx
, isl_space_is_equal(qp1
->dim
, qp2
->dim
), goto error
);
1429 if (!compatible_divs(qp1
->div
, qp2
->div
))
1430 return with_merged_divs(isl_qpolynomial_add
, qp1
, qp2
);
1432 qp1
->upoly
= isl_upoly_sum(qp1
->upoly
, isl_upoly_copy(qp2
->upoly
));
1436 isl_qpolynomial_free(qp2
);
1440 isl_qpolynomial_free(qp1
);
1441 isl_qpolynomial_free(qp2
);
1445 __isl_give isl_qpolynomial
*isl_qpolynomial_add_on_domain(
1446 __isl_keep isl_set
*dom
,
1447 __isl_take isl_qpolynomial
*qp1
,
1448 __isl_take isl_qpolynomial
*qp2
)
1450 qp1
= isl_qpolynomial_add(qp1
, qp2
);
1451 qp1
= isl_qpolynomial_gist(qp1
, isl_set_copy(dom
));
1455 __isl_give isl_qpolynomial
*isl_qpolynomial_sub(__isl_take isl_qpolynomial
*qp1
,
1456 __isl_take isl_qpolynomial
*qp2
)
1458 return isl_qpolynomial_add(qp1
, isl_qpolynomial_neg(qp2
));
1461 __isl_give isl_qpolynomial
*isl_qpolynomial_add_isl_int(
1462 __isl_take isl_qpolynomial
*qp
, isl_int v
)
1464 if (isl_int_is_zero(v
))
1467 qp
= isl_qpolynomial_cow(qp
);
1471 qp
->upoly
= isl_upoly_add_isl_int(qp
->upoly
, v
);
1477 isl_qpolynomial_free(qp
);
1482 __isl_give isl_qpolynomial
*isl_qpolynomial_neg(__isl_take isl_qpolynomial
*qp
)
1487 return isl_qpolynomial_mul_isl_int(qp
, qp
->dim
->ctx
->negone
);
1490 __isl_give isl_qpolynomial
*isl_qpolynomial_mul_isl_int(
1491 __isl_take isl_qpolynomial
*qp
, isl_int v
)
1493 if (isl_int_is_one(v
))
1496 if (qp
&& isl_int_is_zero(v
)) {
1497 isl_qpolynomial
*zero
;
1498 zero
= isl_qpolynomial_zero_on_domain(isl_space_copy(qp
->dim
));
1499 isl_qpolynomial_free(qp
);
1503 qp
= isl_qpolynomial_cow(qp
);
1507 qp
->upoly
= isl_upoly_mul_isl_int(qp
->upoly
, v
);
1513 isl_qpolynomial_free(qp
);
1517 __isl_give isl_qpolynomial
*isl_qpolynomial_scale(
1518 __isl_take isl_qpolynomial
*qp
, isl_int v
)
1520 return isl_qpolynomial_mul_isl_int(qp
, v
);
1523 /* Multiply "qp" by "v".
1525 __isl_give isl_qpolynomial
*isl_qpolynomial_scale_val(
1526 __isl_take isl_qpolynomial
*qp
, __isl_take isl_val
*v
)
1531 if (!isl_val_is_rat(v
))
1532 isl_die(isl_qpolynomial_get_ctx(qp
), isl_error_invalid
,
1533 "expecting rational factor", goto error
);
1535 if (isl_val_is_one(v
)) {
1540 if (isl_val_is_zero(v
)) {
1543 space
= isl_qpolynomial_get_domain_space(qp
);
1544 isl_qpolynomial_free(qp
);
1546 return isl_qpolynomial_zero_on_domain(space
);
1549 qp
= isl_qpolynomial_cow(qp
);
1553 qp
->upoly
= isl_upoly_scale_val(qp
->upoly
, v
);
1555 qp
= isl_qpolynomial_free(qp
);
1561 isl_qpolynomial_free(qp
);
1565 __isl_give isl_qpolynomial
*isl_qpolynomial_mul(__isl_take isl_qpolynomial
*qp1
,
1566 __isl_take isl_qpolynomial
*qp2
)
1568 qp1
= isl_qpolynomial_cow(qp1
);
1573 if (qp1
->div
->n_row
< qp2
->div
->n_row
)
1574 return isl_qpolynomial_mul(qp2
, qp1
);
1576 isl_assert(qp1
->dim
->ctx
, isl_space_is_equal(qp1
->dim
, qp2
->dim
), goto error
);
1577 if (!compatible_divs(qp1
->div
, qp2
->div
))
1578 return with_merged_divs(isl_qpolynomial_mul
, qp1
, qp2
);
1580 qp1
->upoly
= isl_upoly_mul(qp1
->upoly
, isl_upoly_copy(qp2
->upoly
));
1584 isl_qpolynomial_free(qp2
);
1588 isl_qpolynomial_free(qp1
);
1589 isl_qpolynomial_free(qp2
);
1593 __isl_give isl_qpolynomial
*isl_qpolynomial_pow(__isl_take isl_qpolynomial
*qp
,
1596 qp
= isl_qpolynomial_cow(qp
);
1601 qp
->upoly
= isl_upoly_pow(qp
->upoly
, power
);
1607 isl_qpolynomial_free(qp
);
1611 __isl_give isl_pw_qpolynomial
*isl_pw_qpolynomial_pow(
1612 __isl_take isl_pw_qpolynomial
*pwqp
, unsigned power
)
1619 pwqp
= isl_pw_qpolynomial_cow(pwqp
);
1623 for (i
= 0; i
< pwqp
->n
; ++i
) {
1624 pwqp
->p
[i
].qp
= isl_qpolynomial_pow(pwqp
->p
[i
].qp
, power
);
1626 return isl_pw_qpolynomial_free(pwqp
);
1632 __isl_give isl_qpolynomial
*isl_qpolynomial_zero_on_domain(
1633 __isl_take isl_space
*dim
)
1637 return isl_qpolynomial_alloc(dim
, 0, isl_upoly_zero(dim
->ctx
));
1640 __isl_give isl_qpolynomial
*isl_qpolynomial_one_on_domain(
1641 __isl_take isl_space
*dim
)
1645 return isl_qpolynomial_alloc(dim
, 0, isl_upoly_one(dim
->ctx
));
1648 __isl_give isl_qpolynomial
*isl_qpolynomial_infty_on_domain(
1649 __isl_take isl_space
*dim
)
1653 return isl_qpolynomial_alloc(dim
, 0, isl_upoly_infty(dim
->ctx
));
1656 __isl_give isl_qpolynomial
*isl_qpolynomial_neginfty_on_domain(
1657 __isl_take isl_space
*dim
)
1661 return isl_qpolynomial_alloc(dim
, 0, isl_upoly_neginfty(dim
->ctx
));
1664 __isl_give isl_qpolynomial
*isl_qpolynomial_nan_on_domain(
1665 __isl_take isl_space
*dim
)
1669 return isl_qpolynomial_alloc(dim
, 0, isl_upoly_nan(dim
->ctx
));
1672 __isl_give isl_qpolynomial
*isl_qpolynomial_cst_on_domain(
1673 __isl_take isl_space
*dim
,
1676 struct isl_qpolynomial
*qp
;
1677 struct isl_upoly_cst
*cst
;
1682 qp
= isl_qpolynomial_alloc(dim
, 0, isl_upoly_zero(dim
->ctx
));
1686 cst
= isl_upoly_as_cst(qp
->upoly
);
1687 isl_int_set(cst
->n
, v
);
1692 int isl_qpolynomial_is_cst(__isl_keep isl_qpolynomial
*qp
,
1693 isl_int
*n
, isl_int
*d
)
1695 struct isl_upoly_cst
*cst
;
1700 if (!isl_upoly_is_cst(qp
->upoly
))
1703 cst
= isl_upoly_as_cst(qp
->upoly
);
1708 isl_int_set(*n
, cst
->n
);
1710 isl_int_set(*d
, cst
->d
);
1715 /* Return the constant term of "up".
1717 static __isl_give isl_val
*isl_upoly_get_constant_val(
1718 __isl_keep
struct isl_upoly
*up
)
1720 struct isl_upoly_cst
*cst
;
1725 while (!isl_upoly_is_cst(up
)) {
1726 struct isl_upoly_rec
*rec
;
1728 rec
= isl_upoly_as_rec(up
);
1734 cst
= isl_upoly_as_cst(up
);
1737 return isl_val_rat_from_isl_int(cst
->up
.ctx
, cst
->n
, cst
->d
);
1740 /* Return the constant term of "qp".
1742 __isl_give isl_val
*isl_qpolynomial_get_constant_val(
1743 __isl_keep isl_qpolynomial
*qp
)
1748 return isl_upoly_get_constant_val(qp
->upoly
);
1751 int isl_upoly_is_affine(__isl_keep
struct isl_upoly
*up
)
1754 struct isl_upoly_rec
*rec
;
1762 rec
= isl_upoly_as_rec(up
);
1769 isl_assert(up
->ctx
, rec
->n
> 1, return -1);
1771 is_cst
= isl_upoly_is_cst(rec
->p
[1]);
1777 return isl_upoly_is_affine(rec
->p
[0]);
1780 int isl_qpolynomial_is_affine(__isl_keep isl_qpolynomial
*qp
)
1785 if (qp
->div
->n_row
> 0)
1788 return isl_upoly_is_affine(qp
->upoly
);
1791 static void update_coeff(__isl_keep isl_vec
*aff
,
1792 __isl_keep
struct isl_upoly_cst
*cst
, int pos
)
1797 if (isl_int_is_zero(cst
->n
))
1802 isl_int_gcd(gcd
, cst
->d
, aff
->el
[0]);
1803 isl_int_divexact(f
, cst
->d
, gcd
);
1804 isl_int_divexact(gcd
, aff
->el
[0], gcd
);
1805 isl_seq_scale(aff
->el
, aff
->el
, f
, aff
->size
);
1806 isl_int_mul(aff
->el
[1 + pos
], gcd
, cst
->n
);
1811 int isl_upoly_update_affine(__isl_keep
struct isl_upoly
*up
,
1812 __isl_keep isl_vec
*aff
)
1814 struct isl_upoly_cst
*cst
;
1815 struct isl_upoly_rec
*rec
;
1821 struct isl_upoly_cst
*cst
;
1823 cst
= isl_upoly_as_cst(up
);
1826 update_coeff(aff
, cst
, 0);
1830 rec
= isl_upoly_as_rec(up
);
1833 isl_assert(up
->ctx
, rec
->n
== 2, return -1);
1835 cst
= isl_upoly_as_cst(rec
->p
[1]);
1838 update_coeff(aff
, cst
, 1 + up
->var
);
1840 return isl_upoly_update_affine(rec
->p
[0], aff
);
1843 __isl_give isl_vec
*isl_qpolynomial_extract_affine(
1844 __isl_keep isl_qpolynomial
*qp
)
1852 d
= isl_space_dim(qp
->dim
, isl_dim_all
);
1853 aff
= isl_vec_alloc(qp
->div
->ctx
, 2 + d
+ qp
->div
->n_row
);
1857 isl_seq_clr(aff
->el
+ 1, 1 + d
+ qp
->div
->n_row
);
1858 isl_int_set_si(aff
->el
[0], 1);
1860 if (isl_upoly_update_affine(qp
->upoly
, aff
) < 0)
1869 int isl_qpolynomial_plain_is_equal(__isl_keep isl_qpolynomial
*qp1
,
1870 __isl_keep isl_qpolynomial
*qp2
)
1877 equal
= isl_space_is_equal(qp1
->dim
, qp2
->dim
);
1878 if (equal
< 0 || !equal
)
1881 equal
= isl_mat_is_equal(qp1
->div
, qp2
->div
);
1882 if (equal
< 0 || !equal
)
1885 return isl_upoly_is_equal(qp1
->upoly
, qp2
->upoly
);
1888 static void upoly_update_den(__isl_keep
struct isl_upoly
*up
, isl_int
*d
)
1891 struct isl_upoly_rec
*rec
;
1893 if (isl_upoly_is_cst(up
)) {
1894 struct isl_upoly_cst
*cst
;
1895 cst
= isl_upoly_as_cst(up
);
1898 isl_int_lcm(*d
, *d
, cst
->d
);
1902 rec
= isl_upoly_as_rec(up
);
1906 for (i
= 0; i
< rec
->n
; ++i
)
1907 upoly_update_den(rec
->p
[i
], d
);
1910 void isl_qpolynomial_get_den(__isl_keep isl_qpolynomial
*qp
, isl_int
*d
)
1912 isl_int_set_si(*d
, 1);
1915 upoly_update_den(qp
->upoly
, d
);
1918 __isl_give isl_qpolynomial
*isl_qpolynomial_var_pow_on_domain(
1919 __isl_take isl_space
*dim
, int pos
, int power
)
1921 struct isl_ctx
*ctx
;
1928 return isl_qpolynomial_alloc(dim
, 0, isl_upoly_var_pow(ctx
, pos
, power
));
1931 __isl_give isl_qpolynomial
*isl_qpolynomial_var_on_domain(__isl_take isl_space
*dim
,
1932 enum isl_dim_type type
, unsigned pos
)
1937 isl_assert(dim
->ctx
, isl_space_dim(dim
, isl_dim_in
) == 0, goto error
);
1938 isl_assert(dim
->ctx
, pos
< isl_space_dim(dim
, type
), goto error
);
1940 if (type
== isl_dim_set
)
1941 pos
+= isl_space_dim(dim
, isl_dim_param
);
1943 return isl_qpolynomial_var_pow_on_domain(dim
, pos
, 1);
1945 isl_space_free(dim
);
1949 __isl_give
struct isl_upoly
*isl_upoly_subs(__isl_take
struct isl_upoly
*up
,
1950 unsigned first
, unsigned n
, __isl_keep
struct isl_upoly
**subs
)
1953 struct isl_upoly_rec
*rec
;
1954 struct isl_upoly
*base
, *res
;
1959 if (isl_upoly_is_cst(up
))
1962 if (up
->var
< first
)
1965 rec
= isl_upoly_as_rec(up
);
1969 isl_assert(up
->ctx
, rec
->n
>= 1, goto error
);
1971 if (up
->var
>= first
+ n
)
1972 base
= isl_upoly_var_pow(up
->ctx
, up
->var
, 1);
1974 base
= isl_upoly_copy(subs
[up
->var
- first
]);
1976 res
= isl_upoly_subs(isl_upoly_copy(rec
->p
[rec
->n
- 1]), first
, n
, subs
);
1977 for (i
= rec
->n
- 2; i
>= 0; --i
) {
1978 struct isl_upoly
*t
;
1979 t
= isl_upoly_subs(isl_upoly_copy(rec
->p
[i
]), first
, n
, subs
);
1980 res
= isl_upoly_mul(res
, isl_upoly_copy(base
));
1981 res
= isl_upoly_sum(res
, t
);
1984 isl_upoly_free(base
);
1993 __isl_give
struct isl_upoly
*isl_upoly_from_affine(isl_ctx
*ctx
, isl_int
*f
,
1994 isl_int denom
, unsigned len
)
1997 struct isl_upoly
*up
;
1999 isl_assert(ctx
, len
>= 1, return NULL
);
2001 up
= isl_upoly_rat_cst(ctx
, f
[0], denom
);
2002 for (i
= 0; i
< len
- 1; ++i
) {
2003 struct isl_upoly
*t
;
2004 struct isl_upoly
*c
;
2006 if (isl_int_is_zero(f
[1 + i
]))
2009 c
= isl_upoly_rat_cst(ctx
, f
[1 + i
], denom
);
2010 t
= isl_upoly_var_pow(ctx
, i
, 1);
2011 t
= isl_upoly_mul(c
, t
);
2012 up
= isl_upoly_sum(up
, t
);
2018 /* Remove common factor of non-constant terms and denominator.
2020 static void normalize_div(__isl_keep isl_qpolynomial
*qp
, int div
)
2022 isl_ctx
*ctx
= qp
->div
->ctx
;
2023 unsigned total
= qp
->div
->n_col
- 2;
2025 isl_seq_gcd(qp
->div
->row
[div
] + 2, total
, &ctx
->normalize_gcd
);
2026 isl_int_gcd(ctx
->normalize_gcd
,
2027 ctx
->normalize_gcd
, qp
->div
->row
[div
][0]);
2028 if (isl_int_is_one(ctx
->normalize_gcd
))
2031 isl_seq_scale_down(qp
->div
->row
[div
] + 2, qp
->div
->row
[div
] + 2,
2032 ctx
->normalize_gcd
, total
);
2033 isl_int_divexact(qp
->div
->row
[div
][0], qp
->div
->row
[div
][0],
2034 ctx
->normalize_gcd
);
2035 isl_int_fdiv_q(qp
->div
->row
[div
][1], qp
->div
->row
[div
][1],
2036 ctx
->normalize_gcd
);
2039 /* Replace the integer division identified by "div" by the polynomial "s".
2040 * The integer division is assumed not to appear in the definition
2041 * of any other integer divisions.
2043 static __isl_give isl_qpolynomial
*substitute_div(
2044 __isl_take isl_qpolynomial
*qp
,
2045 int div
, __isl_take
struct isl_upoly
*s
)
2054 qp
= isl_qpolynomial_cow(qp
);
2058 total
= isl_space_dim(qp
->dim
, isl_dim_all
);
2059 qp
->upoly
= isl_upoly_subs(qp
->upoly
, total
+ div
, 1, &s
);
2063 reordering
= isl_alloc_array(qp
->dim
->ctx
, int, total
+ qp
->div
->n_row
);
2066 for (i
= 0; i
< total
+ div
; ++i
)
2068 for (i
= total
+ div
+ 1; i
< total
+ qp
->div
->n_row
; ++i
)
2069 reordering
[i
] = i
- 1;
2070 qp
->div
= isl_mat_drop_rows(qp
->div
, div
, 1);
2071 qp
->div
= isl_mat_drop_cols(qp
->div
, 2 + total
+ div
, 1);
2072 qp
->upoly
= reorder(qp
->upoly
, reordering
);
2075 if (!qp
->upoly
|| !qp
->div
)
2081 isl_qpolynomial_free(qp
);
2086 /* Replace all integer divisions [e/d] that turn out to not actually be integer
2087 * divisions because d is equal to 1 by their definition, i.e., e.
2089 static __isl_give isl_qpolynomial
*substitute_non_divs(
2090 __isl_take isl_qpolynomial
*qp
)
2094 struct isl_upoly
*s
;
2099 total
= isl_space_dim(qp
->dim
, isl_dim_all
);
2100 for (i
= 0; qp
&& i
< qp
->div
->n_row
; ++i
) {
2101 if (!isl_int_is_one(qp
->div
->row
[i
][0]))
2103 for (j
= i
+ 1; j
< qp
->div
->n_row
; ++j
) {
2104 if (isl_int_is_zero(qp
->div
->row
[j
][2 + total
+ i
]))
2106 isl_seq_combine(qp
->div
->row
[j
] + 1,
2107 qp
->div
->ctx
->one
, qp
->div
->row
[j
] + 1,
2108 qp
->div
->row
[j
][2 + total
+ i
],
2109 qp
->div
->row
[i
] + 1, 1 + total
+ i
);
2110 isl_int_set_si(qp
->div
->row
[j
][2 + total
+ i
], 0);
2111 normalize_div(qp
, j
);
2113 s
= isl_upoly_from_affine(qp
->dim
->ctx
, qp
->div
->row
[i
] + 1,
2114 qp
->div
->row
[i
][0], qp
->div
->n_col
- 1);
2115 qp
= substitute_div(qp
, i
, s
);
2122 /* Reduce the coefficients of div "div" to lie in the interval [0, d-1],
2123 * with d the denominator. When replacing the coefficient e of x by
2124 * d * frac(e/d) = e - d * floor(e/d), we are subtracting d * floor(e/d) * x
2125 * inside the division, so we need to add floor(e/d) * x outside.
2126 * That is, we replace q by q' + floor(e/d) * x and we therefore need
2127 * to adjust the coefficient of x in each later div that depends on the
2128 * current div "div" and also in the affine expression "aff"
2129 * (if it too depends on "div").
2131 static void reduce_div(__isl_keep isl_qpolynomial
*qp
, int div
,
2132 __isl_keep isl_vec
*aff
)
2136 unsigned total
= qp
->div
->n_col
- qp
->div
->n_row
- 2;
2139 for (i
= 0; i
< 1 + total
+ div
; ++i
) {
2140 if (isl_int_is_nonneg(qp
->div
->row
[div
][1 + i
]) &&
2141 isl_int_lt(qp
->div
->row
[div
][1 + i
], qp
->div
->row
[div
][0]))
2143 isl_int_fdiv_q(v
, qp
->div
->row
[div
][1 + i
], qp
->div
->row
[div
][0]);
2144 isl_int_fdiv_r(qp
->div
->row
[div
][1 + i
],
2145 qp
->div
->row
[div
][1 + i
], qp
->div
->row
[div
][0]);
2146 if (!isl_int_is_zero(aff
->el
[1 + total
+ div
]))
2147 isl_int_addmul(aff
->el
[i
], v
, aff
->el
[1 + total
+ div
]);
2148 for (j
= div
+ 1; j
< qp
->div
->n_row
; ++j
) {
2149 if (isl_int_is_zero(qp
->div
->row
[j
][2 + total
+ div
]))
2151 isl_int_addmul(qp
->div
->row
[j
][1 + i
],
2152 v
, qp
->div
->row
[j
][2 + total
+ div
]);
2158 /* Check if the last non-zero coefficient is bigger that half of the
2159 * denominator. If so, we will invert the div to further reduce the number
2160 * of distinct divs that may appear.
2161 * If the last non-zero coefficient is exactly half the denominator,
2162 * then we continue looking for earlier coefficients that are bigger
2163 * than half the denominator.
2165 static int needs_invert(__isl_keep isl_mat
*div
, int row
)
2170 for (i
= div
->n_col
- 1; i
>= 1; --i
) {
2171 if (isl_int_is_zero(div
->row
[row
][i
]))
2173 isl_int_mul_ui(div
->row
[row
][i
], div
->row
[row
][i
], 2);
2174 cmp
= isl_int_cmp(div
->row
[row
][i
], div
->row
[row
][0]);
2175 isl_int_divexact_ui(div
->row
[row
][i
], div
->row
[row
][i
], 2);
2185 /* Replace div "div" q = [e/d] by -[(-e+(d-1))/d].
2186 * We only invert the coefficients of e (and the coefficient of q in
2187 * later divs and in "aff"). After calling this function, the
2188 * coefficients of e should be reduced again.
2190 static void invert_div(__isl_keep isl_qpolynomial
*qp
, int div
,
2191 __isl_keep isl_vec
*aff
)
2193 unsigned total
= qp
->div
->n_col
- qp
->div
->n_row
- 2;
2195 isl_seq_neg(qp
->div
->row
[div
] + 1,
2196 qp
->div
->row
[div
] + 1, qp
->div
->n_col
- 1);
2197 isl_int_sub_ui(qp
->div
->row
[div
][1], qp
->div
->row
[div
][1], 1);
2198 isl_int_add(qp
->div
->row
[div
][1],
2199 qp
->div
->row
[div
][1], qp
->div
->row
[div
][0]);
2200 if (!isl_int_is_zero(aff
->el
[1 + total
+ div
]))
2201 isl_int_neg(aff
->el
[1 + total
+ div
], aff
->el
[1 + total
+ div
]);
2202 isl_mat_col_mul(qp
->div
, 2 + total
+ div
,
2203 qp
->div
->ctx
->negone
, 2 + total
+ div
);
2206 /* Assuming "qp" is a monomial, reduce all its divs to have coefficients
2207 * in the interval [0, d-1], with d the denominator and such that the
2208 * last non-zero coefficient that is not equal to d/2 is smaller than d/2.
2210 * After the reduction, some divs may have become redundant or identical,
2211 * so we call substitute_non_divs and sort_divs. If these functions
2212 * eliminate divs or merge two or more divs into one, the coefficients
2213 * of the enclosing divs may have to be reduced again, so we call
2214 * ourselves recursively if the number of divs decreases.
2216 static __isl_give isl_qpolynomial
*reduce_divs(__isl_take isl_qpolynomial
*qp
)
2219 isl_vec
*aff
= NULL
;
2220 struct isl_upoly
*s
;
2226 aff
= isl_vec_alloc(qp
->div
->ctx
, qp
->div
->n_col
- 1);
2227 aff
= isl_vec_clr(aff
);
2231 isl_int_set_si(aff
->el
[1 + qp
->upoly
->var
], 1);
2233 for (i
= 0; i
< qp
->div
->n_row
; ++i
) {
2234 normalize_div(qp
, i
);
2235 reduce_div(qp
, i
, aff
);
2236 if (needs_invert(qp
->div
, i
)) {
2237 invert_div(qp
, i
, aff
);
2238 reduce_div(qp
, i
, aff
);
2242 s
= isl_upoly_from_affine(qp
->div
->ctx
, aff
->el
,
2243 qp
->div
->ctx
->one
, aff
->size
);
2244 qp
->upoly
= isl_upoly_subs(qp
->upoly
, qp
->upoly
->var
, 1, &s
);
2251 n_div
= qp
->div
->n_row
;
2252 qp
= substitute_non_divs(qp
);
2254 if (qp
&& qp
->div
->n_row
< n_div
)
2255 return reduce_divs(qp
);
2259 isl_qpolynomial_free(qp
);
2264 __isl_give isl_qpolynomial
*isl_qpolynomial_rat_cst_on_domain(
2265 __isl_take isl_space
*dim
, const isl_int n
, const isl_int d
)
2267 struct isl_qpolynomial
*qp
;
2268 struct isl_upoly_cst
*cst
;
2273 qp
= isl_qpolynomial_alloc(dim
, 0, isl_upoly_zero(dim
->ctx
));
2277 cst
= isl_upoly_as_cst(qp
->upoly
);
2278 isl_int_set(cst
->n
, n
);
2279 isl_int_set(cst
->d
, d
);
2284 /* Return an isl_qpolynomial that is equal to "val" on domain space "domain".
2286 __isl_give isl_qpolynomial
*isl_qpolynomial_val_on_domain(
2287 __isl_take isl_space
*domain
, __isl_take isl_val
*val
)
2289 isl_qpolynomial
*qp
;
2290 struct isl_upoly_cst
*cst
;
2292 if (!domain
|| !val
)
2295 qp
= isl_qpolynomial_alloc(domain
, 0, isl_upoly_zero(domain
->ctx
));
2299 cst
= isl_upoly_as_cst(qp
->upoly
);
2300 isl_int_set(cst
->n
, val
->n
);
2301 isl_int_set(cst
->d
, val
->d
);
2306 isl_space_free(domain
);
2311 static int up_set_active(__isl_keep
struct isl_upoly
*up
, int *active
, int d
)
2313 struct isl_upoly_rec
*rec
;
2319 if (isl_upoly_is_cst(up
))
2323 active
[up
->var
] = 1;
2325 rec
= isl_upoly_as_rec(up
);
2326 for (i
= 0; i
< rec
->n
; ++i
)
2327 if (up_set_active(rec
->p
[i
], active
, d
) < 0)
2333 static int set_active(__isl_keep isl_qpolynomial
*qp
, int *active
)
2336 int d
= isl_space_dim(qp
->dim
, isl_dim_all
);
2341 for (i
= 0; i
< d
; ++i
)
2342 for (j
= 0; j
< qp
->div
->n_row
; ++j
) {
2343 if (isl_int_is_zero(qp
->div
->row
[j
][2 + i
]))
2349 return up_set_active(qp
->upoly
, active
, d
);
2352 int isl_qpolynomial_involves_dims(__isl_keep isl_qpolynomial
*qp
,
2353 enum isl_dim_type type
, unsigned first
, unsigned n
)
2364 isl_assert(qp
->dim
->ctx
,
2365 first
+ n
<= isl_qpolynomial_dim(qp
, type
), return -1);
2366 isl_assert(qp
->dim
->ctx
, type
== isl_dim_param
||
2367 type
== isl_dim_in
, return -1);
2369 active
= isl_calloc_array(qp
->dim
->ctx
, int,
2370 isl_space_dim(qp
->dim
, isl_dim_all
));
2371 if (set_active(qp
, active
) < 0)
2374 if (type
== isl_dim_in
)
2375 first
+= isl_space_dim(qp
->dim
, isl_dim_param
);
2376 for (i
= 0; i
< n
; ++i
)
2377 if (active
[first
+ i
]) {
2390 /* Remove divs that do not appear in the quasi-polynomial, nor in any
2391 * of the divs that do appear in the quasi-polynomial.
2393 static __isl_give isl_qpolynomial
*remove_redundant_divs(
2394 __isl_take isl_qpolynomial
*qp
)
2401 int *reordering
= NULL
;
2408 if (qp
->div
->n_row
== 0)
2411 d
= isl_space_dim(qp
->dim
, isl_dim_all
);
2412 len
= qp
->div
->n_col
- 2;
2413 ctx
= isl_qpolynomial_get_ctx(qp
);
2414 active
= isl_calloc_array(ctx
, int, len
);
2418 if (up_set_active(qp
->upoly
, active
, len
) < 0)
2421 for (i
= qp
->div
->n_row
- 1; i
>= 0; --i
) {
2422 if (!active
[d
+ i
]) {
2426 for (j
= 0; j
< i
; ++j
) {
2427 if (isl_int_is_zero(qp
->div
->row
[i
][2 + d
+ j
]))
2439 reordering
= isl_alloc_array(qp
->div
->ctx
, int, len
);
2443 for (i
= 0; i
< d
; ++i
)
2447 n_div
= qp
->div
->n_row
;
2448 for (i
= 0; i
< n_div
; ++i
) {
2449 if (!active
[d
+ i
]) {
2450 qp
->div
= isl_mat_drop_rows(qp
->div
, i
- skip
, 1);
2451 qp
->div
= isl_mat_drop_cols(qp
->div
,
2452 2 + d
+ i
- skip
, 1);
2455 reordering
[d
+ i
] = d
+ i
- skip
;
2458 qp
->upoly
= reorder(qp
->upoly
, reordering
);
2460 if (!qp
->upoly
|| !qp
->div
)
2470 isl_qpolynomial_free(qp
);
2474 __isl_give
struct isl_upoly
*isl_upoly_drop(__isl_take
struct isl_upoly
*up
,
2475 unsigned first
, unsigned n
)
2478 struct isl_upoly_rec
*rec
;
2482 if (n
== 0 || up
->var
< 0 || up
->var
< first
)
2484 if (up
->var
< first
+ n
) {
2485 up
= replace_by_constant_term(up
);
2486 return isl_upoly_drop(up
, first
, n
);
2488 up
= isl_upoly_cow(up
);
2492 rec
= isl_upoly_as_rec(up
);
2496 for (i
= 0; i
< rec
->n
; ++i
) {
2497 rec
->p
[i
] = isl_upoly_drop(rec
->p
[i
], first
, n
);
2508 __isl_give isl_qpolynomial
*isl_qpolynomial_set_dim_name(
2509 __isl_take isl_qpolynomial
*qp
,
2510 enum isl_dim_type type
, unsigned pos
, const char *s
)
2512 qp
= isl_qpolynomial_cow(qp
);
2515 qp
->dim
= isl_space_set_dim_name(qp
->dim
, type
, pos
, s
);
2520 isl_qpolynomial_free(qp
);
2524 __isl_give isl_qpolynomial
*isl_qpolynomial_drop_dims(
2525 __isl_take isl_qpolynomial
*qp
,
2526 enum isl_dim_type type
, unsigned first
, unsigned n
)
2530 if (type
== isl_dim_out
)
2531 isl_die(qp
->dim
->ctx
, isl_error_invalid
,
2532 "cannot drop output/set dimension",
2534 if (type
== isl_dim_in
)
2536 if (n
== 0 && !isl_space_is_named_or_nested(qp
->dim
, type
))
2539 qp
= isl_qpolynomial_cow(qp
);
2543 isl_assert(qp
->dim
->ctx
, first
+ n
<= isl_space_dim(qp
->dim
, type
),
2545 isl_assert(qp
->dim
->ctx
, type
== isl_dim_param
||
2546 type
== isl_dim_set
, goto error
);
2548 qp
->dim
= isl_space_drop_dims(qp
->dim
, type
, first
, n
);
2552 if (type
== isl_dim_set
)
2553 first
+= isl_space_dim(qp
->dim
, isl_dim_param
);
2555 qp
->div
= isl_mat_drop_cols(qp
->div
, 2 + first
, n
);
2559 qp
->upoly
= isl_upoly_drop(qp
->upoly
, first
, n
);
2565 isl_qpolynomial_free(qp
);
2569 /* Project the domain of the quasi-polynomial onto its parameter space.
2570 * The quasi-polynomial may not involve any of the domain dimensions.
2572 __isl_give isl_qpolynomial
*isl_qpolynomial_project_domain_on_params(
2573 __isl_take isl_qpolynomial
*qp
)
2579 n
= isl_qpolynomial_dim(qp
, isl_dim_in
);
2580 involves
= isl_qpolynomial_involves_dims(qp
, isl_dim_in
, 0, n
);
2582 return isl_qpolynomial_free(qp
);
2584 isl_die(isl_qpolynomial_get_ctx(qp
), isl_error_invalid
,
2585 "polynomial involves some of the domain dimensions",
2586 return isl_qpolynomial_free(qp
));
2587 qp
= isl_qpolynomial_drop_dims(qp
, isl_dim_in
, 0, n
);
2588 space
= isl_qpolynomial_get_domain_space(qp
);
2589 space
= isl_space_params(space
);
2590 qp
= isl_qpolynomial_reset_domain_space(qp
, space
);
2594 static __isl_give isl_qpolynomial
*isl_qpolynomial_substitute_equalities_lifted(
2595 __isl_take isl_qpolynomial
*qp
, __isl_take isl_basic_set
*eq
)
2601 struct isl_upoly
*up
;
2605 if (eq
->n_eq
== 0) {
2606 isl_basic_set_free(eq
);
2610 qp
= isl_qpolynomial_cow(qp
);
2613 qp
->div
= isl_mat_cow(qp
->div
);
2617 total
= 1 + isl_space_dim(eq
->dim
, isl_dim_all
);
2619 isl_int_init(denom
);
2620 for (i
= 0; i
< eq
->n_eq
; ++i
) {
2621 j
= isl_seq_last_non_zero(eq
->eq
[i
], total
+ n_div
);
2622 if (j
< 0 || j
== 0 || j
>= total
)
2625 for (k
= 0; k
< qp
->div
->n_row
; ++k
) {
2626 if (isl_int_is_zero(qp
->div
->row
[k
][1 + j
]))
2628 isl_seq_elim(qp
->div
->row
[k
] + 1, eq
->eq
[i
], j
, total
,
2629 &qp
->div
->row
[k
][0]);
2630 normalize_div(qp
, k
);
2633 if (isl_int_is_pos(eq
->eq
[i
][j
]))
2634 isl_seq_neg(eq
->eq
[i
], eq
->eq
[i
], total
);
2635 isl_int_abs(denom
, eq
->eq
[i
][j
]);
2636 isl_int_set_si(eq
->eq
[i
][j
], 0);
2638 up
= isl_upoly_from_affine(qp
->dim
->ctx
,
2639 eq
->eq
[i
], denom
, total
);
2640 qp
->upoly
= isl_upoly_subs(qp
->upoly
, j
- 1, 1, &up
);
2643 isl_int_clear(denom
);
2648 isl_basic_set_free(eq
);
2650 qp
= substitute_non_divs(qp
);
2655 isl_basic_set_free(eq
);
2656 isl_qpolynomial_free(qp
);
2660 /* Exploit the equalities in "eq" to simplify the quasi-polynomial.
2662 __isl_give isl_qpolynomial
*isl_qpolynomial_substitute_equalities(
2663 __isl_take isl_qpolynomial
*qp
, __isl_take isl_basic_set
*eq
)
2667 if (qp
->div
->n_row
> 0)
2668 eq
= isl_basic_set_add_dims(eq
, isl_dim_set
, qp
->div
->n_row
);
2669 return isl_qpolynomial_substitute_equalities_lifted(qp
, eq
);
2671 isl_basic_set_free(eq
);
2672 isl_qpolynomial_free(qp
);
2676 static __isl_give isl_basic_set
*add_div_constraints(
2677 __isl_take isl_basic_set
*bset
, __isl_take isl_mat
*div
)
2685 bset
= isl_basic_set_extend_constraints(bset
, 0, 2 * div
->n_row
);
2688 total
= isl_basic_set_total_dim(bset
);
2689 for (i
= 0; i
< div
->n_row
; ++i
)
2690 if (isl_basic_set_add_div_constraints_var(bset
,
2691 total
- div
->n_row
+ i
, div
->row
[i
]) < 0)
2698 isl_basic_set_free(bset
);
2702 /* Look for equalities among the variables shared by context and qp
2703 * and the integer divisions of qp, if any.
2704 * The equalities are then used to eliminate variables and/or integer
2705 * divisions from qp.
2707 __isl_give isl_qpolynomial
*isl_qpolynomial_gist(
2708 __isl_take isl_qpolynomial
*qp
, __isl_take isl_set
*context
)
2714 if (qp
->div
->n_row
> 0) {
2715 isl_basic_set
*bset
;
2716 context
= isl_set_add_dims(context
, isl_dim_set
,
2718 bset
= isl_basic_set_universe(isl_set_get_space(context
));
2719 bset
= add_div_constraints(bset
, isl_mat_copy(qp
->div
));
2720 context
= isl_set_intersect(context
,
2721 isl_set_from_basic_set(bset
));
2724 aff
= isl_set_affine_hull(context
);
2725 return isl_qpolynomial_substitute_equalities_lifted(qp
, aff
);
2727 isl_qpolynomial_free(qp
);
2728 isl_set_free(context
);
2732 __isl_give isl_qpolynomial
*isl_qpolynomial_gist_params(
2733 __isl_take isl_qpolynomial
*qp
, __isl_take isl_set
*context
)
2735 isl_space
*space
= isl_qpolynomial_get_domain_space(qp
);
2736 isl_set
*dom_context
= isl_set_universe(space
);
2737 dom_context
= isl_set_intersect_params(dom_context
, context
);
2738 return isl_qpolynomial_gist(qp
, dom_context
);
2741 __isl_give isl_pw_qpolynomial
*isl_pw_qpolynomial_from_qpolynomial(
2742 __isl_take isl_qpolynomial
*qp
)
2748 if (isl_qpolynomial_is_zero(qp
)) {
2749 isl_space
*dim
= isl_qpolynomial_get_space(qp
);
2750 isl_qpolynomial_free(qp
);
2751 return isl_pw_qpolynomial_zero(dim
);
2754 dom
= isl_set_universe(isl_qpolynomial_get_domain_space(qp
));
2755 return isl_pw_qpolynomial_alloc(dom
, qp
);
2759 #define PW isl_pw_qpolynomial
2761 #define EL isl_qpolynomial
2763 #define EL_IS_ZERO is_zero
2767 #define IS_ZERO is_zero
2770 #undef DEFAULT_IS_ZERO
2771 #define DEFAULT_IS_ZERO 1
2775 #include <isl_pw_templ.c>
2778 #define UNION isl_union_pw_qpolynomial
2780 #define PART isl_pw_qpolynomial
2782 #define PARTS pw_qpolynomial
2783 #define ALIGN_DOMAIN
2785 #include <isl_union_templ.c>
2787 int isl_pw_qpolynomial_is_one(__isl_keep isl_pw_qpolynomial
*pwqp
)
2795 if (!isl_set_plain_is_universe(pwqp
->p
[0].set
))
2798 return isl_qpolynomial_is_one(pwqp
->p
[0].qp
);
2801 __isl_give isl_pw_qpolynomial
*isl_pw_qpolynomial_add(
2802 __isl_take isl_pw_qpolynomial
*pwqp1
,
2803 __isl_take isl_pw_qpolynomial
*pwqp2
)
2805 return isl_pw_qpolynomial_union_add_(pwqp1
, pwqp2
);
2808 __isl_give isl_pw_qpolynomial
*isl_pw_qpolynomial_mul(
2809 __isl_take isl_pw_qpolynomial
*pwqp1
,
2810 __isl_take isl_pw_qpolynomial
*pwqp2
)
2813 struct isl_pw_qpolynomial
*res
;
2815 if (!pwqp1
|| !pwqp2
)
2818 isl_assert(pwqp1
->dim
->ctx
, isl_space_is_equal(pwqp1
->dim
, pwqp2
->dim
),
2821 if (isl_pw_qpolynomial_is_zero(pwqp1
)) {
2822 isl_pw_qpolynomial_free(pwqp2
);
2826 if (isl_pw_qpolynomial_is_zero(pwqp2
)) {
2827 isl_pw_qpolynomial_free(pwqp1
);
2831 if (isl_pw_qpolynomial_is_one(pwqp1
)) {
2832 isl_pw_qpolynomial_free(pwqp1
);
2836 if (isl_pw_qpolynomial_is_one(pwqp2
)) {
2837 isl_pw_qpolynomial_free(pwqp2
);
2841 n
= pwqp1
->n
* pwqp2
->n
;
2842 res
= isl_pw_qpolynomial_alloc_size(isl_space_copy(pwqp1
->dim
), n
);
2844 for (i
= 0; i
< pwqp1
->n
; ++i
) {
2845 for (j
= 0; j
< pwqp2
->n
; ++j
) {
2846 struct isl_set
*common
;
2847 struct isl_qpolynomial
*prod
;
2848 common
= isl_set_intersect(isl_set_copy(pwqp1
->p
[i
].set
),
2849 isl_set_copy(pwqp2
->p
[j
].set
));
2850 if (isl_set_plain_is_empty(common
)) {
2851 isl_set_free(common
);
2855 prod
= isl_qpolynomial_mul(
2856 isl_qpolynomial_copy(pwqp1
->p
[i
].qp
),
2857 isl_qpolynomial_copy(pwqp2
->p
[j
].qp
));
2859 res
= isl_pw_qpolynomial_add_piece(res
, common
, prod
);
2863 isl_pw_qpolynomial_free(pwqp1
);
2864 isl_pw_qpolynomial_free(pwqp2
);
2868 isl_pw_qpolynomial_free(pwqp1
);
2869 isl_pw_qpolynomial_free(pwqp2
);
2873 __isl_give
struct isl_upoly
*isl_upoly_eval(
2874 __isl_take
struct isl_upoly
*up
, __isl_take isl_vec
*vec
)
2877 struct isl_upoly_rec
*rec
;
2878 struct isl_upoly
*res
;
2879 struct isl_upoly
*base
;
2881 if (isl_upoly_is_cst(up
)) {
2886 rec
= isl_upoly_as_rec(up
);
2890 isl_assert(up
->ctx
, rec
->n
>= 1, goto error
);
2892 base
= isl_upoly_rat_cst(up
->ctx
, vec
->el
[1 + up
->var
], vec
->el
[0]);
2894 res
= isl_upoly_eval(isl_upoly_copy(rec
->p
[rec
->n
- 1]),
2897 for (i
= rec
->n
- 2; i
>= 0; --i
) {
2898 res
= isl_upoly_mul(res
, isl_upoly_copy(base
));
2899 res
= isl_upoly_sum(res
,
2900 isl_upoly_eval(isl_upoly_copy(rec
->p
[i
]),
2901 isl_vec_copy(vec
)));
2904 isl_upoly_free(base
);
2914 __isl_give isl_qpolynomial
*isl_qpolynomial_eval(
2915 __isl_take isl_qpolynomial
*qp
, __isl_take isl_point
*pnt
)
2918 struct isl_upoly
*up
;
2923 isl_assert(pnt
->dim
->ctx
, isl_space_is_equal(pnt
->dim
, qp
->dim
), goto error
);
2925 if (qp
->div
->n_row
== 0)
2926 ext
= isl_vec_copy(pnt
->vec
);
2929 unsigned dim
= isl_space_dim(qp
->dim
, isl_dim_all
);
2930 ext
= isl_vec_alloc(qp
->dim
->ctx
, 1 + dim
+ qp
->div
->n_row
);
2934 isl_seq_cpy(ext
->el
, pnt
->vec
->el
, pnt
->vec
->size
);
2935 for (i
= 0; i
< qp
->div
->n_row
; ++i
) {
2936 isl_seq_inner_product(qp
->div
->row
[i
] + 1, ext
->el
,
2937 1 + dim
+ i
, &ext
->el
[1+dim
+i
]);
2938 isl_int_fdiv_q(ext
->el
[1+dim
+i
], ext
->el
[1+dim
+i
],
2939 qp
->div
->row
[i
][0]);
2943 up
= isl_upoly_eval(isl_upoly_copy(qp
->upoly
), ext
);
2947 dim
= isl_space_copy(qp
->dim
);
2948 isl_qpolynomial_free(qp
);
2949 isl_point_free(pnt
);
2951 return isl_qpolynomial_alloc(dim
, 0, up
);
2953 isl_qpolynomial_free(qp
);
2954 isl_point_free(pnt
);
2958 int isl_upoly_cmp(__isl_keep
struct isl_upoly_cst
*cst1
,
2959 __isl_keep
struct isl_upoly_cst
*cst2
)
2964 isl_int_mul(t
, cst1
->n
, cst2
->d
);
2965 isl_int_submul(t
, cst2
->n
, cst1
->d
);
2966 cmp
= isl_int_sgn(t
);
2971 int isl_qpolynomial_le_cst(__isl_keep isl_qpolynomial
*qp1
,
2972 __isl_keep isl_qpolynomial
*qp2
)
2974 struct isl_upoly_cst
*cst1
, *cst2
;
2978 isl_assert(qp1
->dim
->ctx
, isl_upoly_is_cst(qp1
->upoly
), return -1);
2979 isl_assert(qp2
->dim
->ctx
, isl_upoly_is_cst(qp2
->upoly
), return -1);
2980 if (isl_qpolynomial_is_nan(qp1
))
2982 if (isl_qpolynomial_is_nan(qp2
))
2984 cst1
= isl_upoly_as_cst(qp1
->upoly
);
2985 cst2
= isl_upoly_as_cst(qp2
->upoly
);
2987 return isl_upoly_cmp(cst1
, cst2
) <= 0;
2990 __isl_give isl_qpolynomial
*isl_qpolynomial_min_cst(
2991 __isl_take isl_qpolynomial
*qp1
, __isl_take isl_qpolynomial
*qp2
)
2993 struct isl_upoly_cst
*cst1
, *cst2
;
2998 isl_assert(qp1
->dim
->ctx
, isl_upoly_is_cst(qp1
->upoly
), goto error
);
2999 isl_assert(qp2
->dim
->ctx
, isl_upoly_is_cst(qp2
->upoly
), goto error
);
3000 cst1
= isl_upoly_as_cst(qp1
->upoly
);
3001 cst2
= isl_upoly_as_cst(qp2
->upoly
);
3002 cmp
= isl_upoly_cmp(cst1
, cst2
);
3005 isl_qpolynomial_free(qp2
);
3007 isl_qpolynomial_free(qp1
);
3012 isl_qpolynomial_free(qp1
);
3013 isl_qpolynomial_free(qp2
);
3017 __isl_give isl_qpolynomial
*isl_qpolynomial_max_cst(
3018 __isl_take isl_qpolynomial
*qp1
, __isl_take isl_qpolynomial
*qp2
)
3020 struct isl_upoly_cst
*cst1
, *cst2
;
3025 isl_assert(qp1
->dim
->ctx
, isl_upoly_is_cst(qp1
->upoly
), goto error
);
3026 isl_assert(qp2
->dim
->ctx
, isl_upoly_is_cst(qp2
->upoly
), goto error
);
3027 cst1
= isl_upoly_as_cst(qp1
->upoly
);
3028 cst2
= isl_upoly_as_cst(qp2
->upoly
);
3029 cmp
= isl_upoly_cmp(cst1
, cst2
);
3032 isl_qpolynomial_free(qp2
);
3034 isl_qpolynomial_free(qp1
);
3039 isl_qpolynomial_free(qp1
);
3040 isl_qpolynomial_free(qp2
);
3044 __isl_give isl_qpolynomial
*isl_qpolynomial_insert_dims(
3045 __isl_take isl_qpolynomial
*qp
, enum isl_dim_type type
,
3046 unsigned first
, unsigned n
)
3054 if (type
== isl_dim_out
)
3055 isl_die(qp
->div
->ctx
, isl_error_invalid
,
3056 "cannot insert output/set dimensions",
3058 if (type
== isl_dim_in
)
3060 if (n
== 0 && !isl_space_is_named_or_nested(qp
->dim
, type
))
3063 qp
= isl_qpolynomial_cow(qp
);
3067 isl_assert(qp
->div
->ctx
, first
<= isl_space_dim(qp
->dim
, type
),
3070 g_pos
= pos(qp
->dim
, type
) + first
;
3072 qp
->div
= isl_mat_insert_zero_cols(qp
->div
, 2 + g_pos
, n
);
3076 total
= qp
->div
->n_col
- 2;
3077 if (total
> g_pos
) {
3079 exp
= isl_alloc_array(qp
->div
->ctx
, int, total
- g_pos
);
3082 for (i
= 0; i
< total
- g_pos
; ++i
)
3084 qp
->upoly
= expand(qp
->upoly
, exp
, g_pos
);
3090 qp
->dim
= isl_space_insert_dims(qp
->dim
, type
, first
, n
);
3096 isl_qpolynomial_free(qp
);
3100 __isl_give isl_qpolynomial
*isl_qpolynomial_add_dims(
3101 __isl_take isl_qpolynomial
*qp
, enum isl_dim_type type
, unsigned n
)
3105 pos
= isl_qpolynomial_dim(qp
, type
);
3107 return isl_qpolynomial_insert_dims(qp
, type
, pos
, n
);
3110 __isl_give isl_pw_qpolynomial
*isl_pw_qpolynomial_add_dims(
3111 __isl_take isl_pw_qpolynomial
*pwqp
,
3112 enum isl_dim_type type
, unsigned n
)
3116 pos
= isl_pw_qpolynomial_dim(pwqp
, type
);
3118 return isl_pw_qpolynomial_insert_dims(pwqp
, type
, pos
, n
);
3121 static int *reordering_move(isl_ctx
*ctx
,
3122 unsigned len
, unsigned dst
, unsigned src
, unsigned n
)
3127 reordering
= isl_alloc_array(ctx
, int, len
);
3132 for (i
= 0; i
< dst
; ++i
)
3134 for (i
= 0; i
< n
; ++i
)
3135 reordering
[src
+ i
] = dst
+ i
;
3136 for (i
= 0; i
< src
- dst
; ++i
)
3137 reordering
[dst
+ i
] = dst
+ n
+ i
;
3138 for (i
= 0; i
< len
- src
- n
; ++i
)
3139 reordering
[src
+ n
+ i
] = src
+ n
+ i
;
3141 for (i
= 0; i
< src
; ++i
)
3143 for (i
= 0; i
< n
; ++i
)
3144 reordering
[src
+ i
] = dst
+ i
;
3145 for (i
= 0; i
< dst
- src
; ++i
)
3146 reordering
[src
+ n
+ i
] = src
+ i
;
3147 for (i
= 0; i
< len
- dst
- n
; ++i
)
3148 reordering
[dst
+ n
+ i
] = dst
+ n
+ i
;
3154 __isl_give isl_qpolynomial
*isl_qpolynomial_move_dims(
3155 __isl_take isl_qpolynomial
*qp
,
3156 enum isl_dim_type dst_type
, unsigned dst_pos
,
3157 enum isl_dim_type src_type
, unsigned src_pos
, unsigned n
)
3163 qp
= isl_qpolynomial_cow(qp
);
3167 if (dst_type
== isl_dim_out
|| src_type
== isl_dim_out
)
3168 isl_die(qp
->dim
->ctx
, isl_error_invalid
,
3169 "cannot move output/set dimension",
3171 if (dst_type
== isl_dim_in
)
3172 dst_type
= isl_dim_set
;
3173 if (src_type
== isl_dim_in
)
3174 src_type
= isl_dim_set
;
3176 isl_assert(qp
->dim
->ctx
, src_pos
+ n
<= isl_space_dim(qp
->dim
, src_type
),
3179 g_dst_pos
= pos(qp
->dim
, dst_type
) + dst_pos
;
3180 g_src_pos
= pos(qp
->dim
, src_type
) + src_pos
;
3181 if (dst_type
> src_type
)
3184 qp
->div
= isl_mat_move_cols(qp
->div
, 2 + g_dst_pos
, 2 + g_src_pos
, n
);
3191 reordering
= reordering_move(qp
->dim
->ctx
,
3192 qp
->div
->n_col
- 2, g_dst_pos
, g_src_pos
, n
);
3196 qp
->upoly
= reorder(qp
->upoly
, reordering
);
3201 qp
->dim
= isl_space_move_dims(qp
->dim
, dst_type
, dst_pos
, src_type
, src_pos
, n
);
3207 isl_qpolynomial_free(qp
);
3211 __isl_give isl_qpolynomial
*isl_qpolynomial_from_affine(__isl_take isl_space
*dim
,
3212 isl_int
*f
, isl_int denom
)
3214 struct isl_upoly
*up
;
3216 dim
= isl_space_domain(dim
);
3220 up
= isl_upoly_from_affine(dim
->ctx
, f
, denom
,
3221 1 + isl_space_dim(dim
, isl_dim_all
));
3223 return isl_qpolynomial_alloc(dim
, 0, up
);
3226 __isl_give isl_qpolynomial
*isl_qpolynomial_from_aff(__isl_take isl_aff
*aff
)
3229 struct isl_upoly
*up
;
3230 isl_qpolynomial
*qp
;
3235 ctx
= isl_aff_get_ctx(aff
);
3236 up
= isl_upoly_from_affine(ctx
, aff
->v
->el
+ 1, aff
->v
->el
[0],
3239 qp
= isl_qpolynomial_alloc(isl_aff_get_domain_space(aff
),
3240 aff
->ls
->div
->n_row
, up
);
3244 isl_mat_free(qp
->div
);
3245 qp
->div
= isl_mat_copy(aff
->ls
->div
);
3246 qp
->div
= isl_mat_cow(qp
->div
);
3251 qp
= reduce_divs(qp
);
3252 qp
= remove_redundant_divs(qp
);
3259 __isl_give isl_pw_qpolynomial
*isl_pw_qpolynomial_from_pw_aff(
3260 __isl_take isl_pw_aff
*pwaff
)
3263 isl_pw_qpolynomial
*pwqp
;
3268 pwqp
= isl_pw_qpolynomial_alloc_size(isl_pw_aff_get_space(pwaff
),
3271 for (i
= 0; i
< pwaff
->n
; ++i
) {
3273 isl_qpolynomial
*qp
;
3275 dom
= isl_set_copy(pwaff
->p
[i
].set
);
3276 qp
= isl_qpolynomial_from_aff(isl_aff_copy(pwaff
->p
[i
].aff
));
3277 pwqp
= isl_pw_qpolynomial_add_piece(pwqp
, dom
, qp
);
3280 isl_pw_aff_free(pwaff
);
3284 __isl_give isl_qpolynomial
*isl_qpolynomial_from_constraint(
3285 __isl_take isl_constraint
*c
, enum isl_dim_type type
, unsigned pos
)
3289 aff
= isl_constraint_get_bound(c
, type
, pos
);
3290 isl_constraint_free(c
);
3291 return isl_qpolynomial_from_aff(aff
);
3294 /* For each 0 <= i < "n", replace variable "first" + i of type "type"
3295 * in "qp" by subs[i].
3297 __isl_give isl_qpolynomial
*isl_qpolynomial_substitute(
3298 __isl_take isl_qpolynomial
*qp
,
3299 enum isl_dim_type type
, unsigned first
, unsigned n
,
3300 __isl_keep isl_qpolynomial
**subs
)
3303 struct isl_upoly
**ups
;
3308 qp
= isl_qpolynomial_cow(qp
);
3312 if (type
== isl_dim_out
)
3313 isl_die(qp
->dim
->ctx
, isl_error_invalid
,
3314 "cannot substitute output/set dimension",
3316 if (type
== isl_dim_in
)
3319 for (i
= 0; i
< n
; ++i
)
3323 isl_assert(qp
->dim
->ctx
, first
+ n
<= isl_space_dim(qp
->dim
, type
),
3326 for (i
= 0; i
< n
; ++i
)
3327 isl_assert(qp
->dim
->ctx
, isl_space_is_equal(qp
->dim
, subs
[i
]->dim
),
3330 isl_assert(qp
->dim
->ctx
, qp
->div
->n_row
== 0, goto error
);
3331 for (i
= 0; i
< n
; ++i
)
3332 isl_assert(qp
->dim
->ctx
, subs
[i
]->div
->n_row
== 0, goto error
);
3334 first
+= pos(qp
->dim
, type
);
3336 ups
= isl_alloc_array(qp
->dim
->ctx
, struct isl_upoly
*, n
);
3339 for (i
= 0; i
< n
; ++i
)
3340 ups
[i
] = subs
[i
]->upoly
;
3342 qp
->upoly
= isl_upoly_subs(qp
->upoly
, first
, n
, ups
);
3351 isl_qpolynomial_free(qp
);
3355 /* Extend "bset" with extra set dimensions for each integer division
3356 * in "qp" and then call "fn" with the extended bset and the polynomial
3357 * that results from replacing each of the integer divisions by the
3358 * corresponding extra set dimension.
3360 int isl_qpolynomial_as_polynomial_on_domain(__isl_keep isl_qpolynomial
*qp
,
3361 __isl_keep isl_basic_set
*bset
,
3362 int (*fn
)(__isl_take isl_basic_set
*bset
,
3363 __isl_take isl_qpolynomial
*poly
, void *user
), void *user
)
3367 isl_qpolynomial
*poly
;
3371 if (qp
->div
->n_row
== 0)
3372 return fn(isl_basic_set_copy(bset
), isl_qpolynomial_copy(qp
),
3375 div
= isl_mat_copy(qp
->div
);
3376 dim
= isl_space_copy(qp
->dim
);
3377 dim
= isl_space_add_dims(dim
, isl_dim_set
, qp
->div
->n_row
);
3378 poly
= isl_qpolynomial_alloc(dim
, 0, isl_upoly_copy(qp
->upoly
));
3379 bset
= isl_basic_set_copy(bset
);
3380 bset
= isl_basic_set_add_dims(bset
, isl_dim_set
, qp
->div
->n_row
);
3381 bset
= add_div_constraints(bset
, div
);
3383 return fn(bset
, poly
, user
);
3388 /* Return total degree in variables first (inclusive) up to last (exclusive).
3390 int isl_upoly_degree(__isl_keep
struct isl_upoly
*up
, int first
, int last
)
3394 struct isl_upoly_rec
*rec
;
3398 if (isl_upoly_is_zero(up
))
3400 if (isl_upoly_is_cst(up
) || up
->var
< first
)
3403 rec
= isl_upoly_as_rec(up
);
3407 for (i
= 0; i
< rec
->n
; ++i
) {
3410 if (isl_upoly_is_zero(rec
->p
[i
]))
3412 d
= isl_upoly_degree(rec
->p
[i
], first
, last
);
3422 /* Return total degree in set variables.
3424 int isl_qpolynomial_degree(__isl_keep isl_qpolynomial
*poly
)
3432 ovar
= isl_space_offset(poly
->dim
, isl_dim_set
);
3433 nvar
= isl_space_dim(poly
->dim
, isl_dim_set
);
3434 return isl_upoly_degree(poly
->upoly
, ovar
, ovar
+ nvar
);
3437 __isl_give
struct isl_upoly
*isl_upoly_coeff(__isl_keep
struct isl_upoly
*up
,
3438 unsigned pos
, int deg
)
3441 struct isl_upoly_rec
*rec
;
3446 if (isl_upoly_is_cst(up
) || up
->var
< pos
) {
3448 return isl_upoly_copy(up
);
3450 return isl_upoly_zero(up
->ctx
);
3453 rec
= isl_upoly_as_rec(up
);
3457 if (up
->var
== pos
) {
3459 return isl_upoly_copy(rec
->p
[deg
]);
3461 return isl_upoly_zero(up
->ctx
);
3464 up
= isl_upoly_copy(up
);
3465 up
= isl_upoly_cow(up
);
3466 rec
= isl_upoly_as_rec(up
);
3470 for (i
= 0; i
< rec
->n
; ++i
) {
3471 struct isl_upoly
*t
;
3472 t
= isl_upoly_coeff(rec
->p
[i
], pos
, deg
);
3475 isl_upoly_free(rec
->p
[i
]);
3485 /* Return coefficient of power "deg" of variable "t_pos" of type "type".
3487 __isl_give isl_qpolynomial
*isl_qpolynomial_coeff(
3488 __isl_keep isl_qpolynomial
*qp
,
3489 enum isl_dim_type type
, unsigned t_pos
, int deg
)
3492 struct isl_upoly
*up
;
3498 if (type
== isl_dim_out
)
3499 isl_die(qp
->div
->ctx
, isl_error_invalid
,
3500 "output/set dimension does not have a coefficient",
3502 if (type
== isl_dim_in
)
3505 isl_assert(qp
->div
->ctx
, t_pos
< isl_space_dim(qp
->dim
, type
),
3508 g_pos
= pos(qp
->dim
, type
) + t_pos
;
3509 up
= isl_upoly_coeff(qp
->upoly
, g_pos
, deg
);
3511 c
= isl_qpolynomial_alloc(isl_space_copy(qp
->dim
), qp
->div
->n_row
, up
);
3514 isl_mat_free(c
->div
);
3515 c
->div
= isl_mat_copy(qp
->div
);
3520 isl_qpolynomial_free(c
);
3524 /* Homogenize the polynomial in the variables first (inclusive) up to
3525 * last (exclusive) by inserting powers of variable first.
3526 * Variable first is assumed not to appear in the input.
3528 __isl_give
struct isl_upoly
*isl_upoly_homogenize(
3529 __isl_take
struct isl_upoly
*up
, int deg
, int target
,
3530 int first
, int last
)
3533 struct isl_upoly_rec
*rec
;
3537 if (isl_upoly_is_zero(up
))
3541 if (isl_upoly_is_cst(up
) || up
->var
< first
) {
3542 struct isl_upoly
*hom
;
3544 hom
= isl_upoly_var_pow(up
->ctx
, first
, target
- deg
);
3547 rec
= isl_upoly_as_rec(hom
);
3548 rec
->p
[target
- deg
] = isl_upoly_mul(rec
->p
[target
- deg
], up
);
3553 up
= isl_upoly_cow(up
);
3554 rec
= isl_upoly_as_rec(up
);
3558 for (i
= 0; i
< rec
->n
; ++i
) {
3559 if (isl_upoly_is_zero(rec
->p
[i
]))
3561 rec
->p
[i
] = isl_upoly_homogenize(rec
->p
[i
],
3562 up
->var
< last
? deg
+ i
: i
, target
,
3574 /* Homogenize the polynomial in the set variables by introducing
3575 * powers of an extra set variable at position 0.
3577 __isl_give isl_qpolynomial
*isl_qpolynomial_homogenize(
3578 __isl_take isl_qpolynomial
*poly
)
3582 int deg
= isl_qpolynomial_degree(poly
);
3587 poly
= isl_qpolynomial_insert_dims(poly
, isl_dim_in
, 0, 1);
3588 poly
= isl_qpolynomial_cow(poly
);
3592 ovar
= isl_space_offset(poly
->dim
, isl_dim_set
);
3593 nvar
= isl_space_dim(poly
->dim
, isl_dim_set
);
3594 poly
->upoly
= isl_upoly_homogenize(poly
->upoly
, 0, deg
,
3601 isl_qpolynomial_free(poly
);
3605 __isl_give isl_term
*isl_term_alloc(__isl_take isl_space
*dim
,
3606 __isl_take isl_mat
*div
)
3614 n
= isl_space_dim(dim
, isl_dim_all
) + div
->n_row
;
3616 term
= isl_calloc(dim
->ctx
, struct isl_term
,
3617 sizeof(struct isl_term
) + (n
- 1) * sizeof(int));
3624 isl_int_init(term
->n
);
3625 isl_int_init(term
->d
);
3629 isl_space_free(dim
);
3634 __isl_give isl_term
*isl_term_copy(__isl_keep isl_term
*term
)
3643 __isl_give isl_term
*isl_term_dup(__isl_keep isl_term
*term
)
3652 total
= isl_space_dim(term
->dim
, isl_dim_all
) + term
->div
->n_row
;
3654 dup
= isl_term_alloc(isl_space_copy(term
->dim
), isl_mat_copy(term
->div
));
3658 isl_int_set(dup
->n
, term
->n
);
3659 isl_int_set(dup
->d
, term
->d
);
3661 for (i
= 0; i
< total
; ++i
)
3662 dup
->pow
[i
] = term
->pow
[i
];
3667 __isl_give isl_term
*isl_term_cow(__isl_take isl_term
*term
)
3675 return isl_term_dup(term
);
3678 void isl_term_free(__isl_take isl_term
*term
)
3683 if (--term
->ref
> 0)
3686 isl_space_free(term
->dim
);
3687 isl_mat_free(term
->div
);
3688 isl_int_clear(term
->n
);
3689 isl_int_clear(term
->d
);
3693 unsigned isl_term_dim(__isl_keep isl_term
*term
, enum isl_dim_type type
)
3701 case isl_dim_out
: return isl_space_dim(term
->dim
, type
);
3702 case isl_dim_div
: return term
->div
->n_row
;
3703 case isl_dim_all
: return isl_space_dim(term
->dim
, isl_dim_all
) +
3709 isl_ctx
*isl_term_get_ctx(__isl_keep isl_term
*term
)
3711 return term
? term
->dim
->ctx
: NULL
;
3714 void isl_term_get_num(__isl_keep isl_term
*term
, isl_int
*n
)
3718 isl_int_set(*n
, term
->n
);
3721 void isl_term_get_den(__isl_keep isl_term
*term
, isl_int
*d
)
3725 isl_int_set(*d
, term
->d
);
3728 /* Return the coefficient of the term "term".
3730 __isl_give isl_val
*isl_term_get_coefficient_val(__isl_keep isl_term
*term
)
3735 return isl_val_rat_from_isl_int(isl_term_get_ctx(term
),
3739 int isl_term_get_exp(__isl_keep isl_term
*term
,
3740 enum isl_dim_type type
, unsigned pos
)
3745 isl_assert(term
->dim
->ctx
, pos
< isl_term_dim(term
, type
), return -1);
3747 if (type
>= isl_dim_set
)
3748 pos
+= isl_space_dim(term
->dim
, isl_dim_param
);
3749 if (type
>= isl_dim_div
)
3750 pos
+= isl_space_dim(term
->dim
, isl_dim_set
);
3752 return term
->pow
[pos
];
3755 __isl_give isl_aff
*isl_term_get_div(__isl_keep isl_term
*term
, unsigned pos
)
3757 isl_local_space
*ls
;
3763 isl_assert(term
->dim
->ctx
, pos
< isl_term_dim(term
, isl_dim_div
),
3766 ls
= isl_local_space_alloc_div(isl_space_copy(term
->dim
),
3767 isl_mat_copy(term
->div
));
3768 aff
= isl_aff_alloc(ls
);
3772 isl_seq_cpy(aff
->v
->el
, term
->div
->row
[pos
], aff
->v
->size
);
3774 aff
= isl_aff_normalize(aff
);
3779 __isl_give isl_term
*isl_upoly_foreach_term(__isl_keep
struct isl_upoly
*up
,
3780 int (*fn
)(__isl_take isl_term
*term
, void *user
),
3781 __isl_take isl_term
*term
, void *user
)
3784 struct isl_upoly_rec
*rec
;
3789 if (isl_upoly_is_zero(up
))
3792 isl_assert(up
->ctx
, !isl_upoly_is_nan(up
), goto error
);
3793 isl_assert(up
->ctx
, !isl_upoly_is_infty(up
), goto error
);
3794 isl_assert(up
->ctx
, !isl_upoly_is_neginfty(up
), goto error
);
3796 if (isl_upoly_is_cst(up
)) {
3797 struct isl_upoly_cst
*cst
;
3798 cst
= isl_upoly_as_cst(up
);
3801 term
= isl_term_cow(term
);
3804 isl_int_set(term
->n
, cst
->n
);
3805 isl_int_set(term
->d
, cst
->d
);
3806 if (fn(isl_term_copy(term
), user
) < 0)
3811 rec
= isl_upoly_as_rec(up
);
3815 for (i
= 0; i
< rec
->n
; ++i
) {
3816 term
= isl_term_cow(term
);
3819 term
->pow
[up
->var
] = i
;
3820 term
= isl_upoly_foreach_term(rec
->p
[i
], fn
, term
, user
);
3824 term
->pow
[up
->var
] = 0;
3828 isl_term_free(term
);
3832 int isl_qpolynomial_foreach_term(__isl_keep isl_qpolynomial
*qp
,
3833 int (*fn
)(__isl_take isl_term
*term
, void *user
), void *user
)
3840 term
= isl_term_alloc(isl_space_copy(qp
->dim
), isl_mat_copy(qp
->div
));
3844 term
= isl_upoly_foreach_term(qp
->upoly
, fn
, term
, user
);
3846 isl_term_free(term
);
3848 return term
? 0 : -1;
3851 __isl_give isl_qpolynomial
*isl_qpolynomial_from_term(__isl_take isl_term
*term
)
3853 struct isl_upoly
*up
;
3854 isl_qpolynomial
*qp
;
3860 n
= isl_space_dim(term
->dim
, isl_dim_all
) + term
->div
->n_row
;
3862 up
= isl_upoly_rat_cst(term
->dim
->ctx
, term
->n
, term
->d
);
3863 for (i
= 0; i
< n
; ++i
) {
3866 up
= isl_upoly_mul(up
,
3867 isl_upoly_var_pow(term
->dim
->ctx
, i
, term
->pow
[i
]));
3870 qp
= isl_qpolynomial_alloc(isl_space_copy(term
->dim
), term
->div
->n_row
, up
);
3873 isl_mat_free(qp
->div
);
3874 qp
->div
= isl_mat_copy(term
->div
);
3878 isl_term_free(term
);
3881 isl_qpolynomial_free(qp
);
3882 isl_term_free(term
);
3886 __isl_give isl_qpolynomial
*isl_qpolynomial_lift(__isl_take isl_qpolynomial
*qp
,
3887 __isl_take isl_space
*dim
)
3896 if (isl_space_is_equal(qp
->dim
, dim
)) {
3897 isl_space_free(dim
);
3901 qp
= isl_qpolynomial_cow(qp
);
3905 extra
= isl_space_dim(dim
, isl_dim_set
) -
3906 isl_space_dim(qp
->dim
, isl_dim_set
);
3907 total
= isl_space_dim(qp
->dim
, isl_dim_all
);
3908 if (qp
->div
->n_row
) {
3911 exp
= isl_alloc_array(qp
->div
->ctx
, int, qp
->div
->n_row
);
3914 for (i
= 0; i
< qp
->div
->n_row
; ++i
)
3916 qp
->upoly
= expand(qp
->upoly
, exp
, total
);
3921 qp
->div
= isl_mat_insert_cols(qp
->div
, 2 + total
, extra
);
3924 for (i
= 0; i
< qp
->div
->n_row
; ++i
)
3925 isl_seq_clr(qp
->div
->row
[i
] + 2 + total
, extra
);
3927 isl_space_free(qp
->dim
);
3932 isl_space_free(dim
);
3933 isl_qpolynomial_free(qp
);
3937 /* For each parameter or variable that does not appear in qp,
3938 * first eliminate the variable from all constraints and then set it to zero.
3940 static __isl_give isl_set
*fix_inactive(__isl_take isl_set
*set
,
3941 __isl_keep isl_qpolynomial
*qp
)
3952 d
= isl_space_dim(set
->dim
, isl_dim_all
);
3953 active
= isl_calloc_array(set
->ctx
, int, d
);
3954 if (set_active(qp
, active
) < 0)
3957 for (i
= 0; i
< d
; ++i
)
3966 nparam
= isl_space_dim(set
->dim
, isl_dim_param
);
3967 nvar
= isl_space_dim(set
->dim
, isl_dim_set
);
3968 for (i
= 0; i
< nparam
; ++i
) {
3971 set
= isl_set_eliminate(set
, isl_dim_param
, i
, 1);
3972 set
= isl_set_fix_si(set
, isl_dim_param
, i
, 0);
3974 for (i
= 0; i
< nvar
; ++i
) {
3975 if (active
[nparam
+ i
])
3977 set
= isl_set_eliminate(set
, isl_dim_set
, i
, 1);
3978 set
= isl_set_fix_si(set
, isl_dim_set
, i
, 0);
3990 struct isl_opt_data
{
3991 isl_qpolynomial
*qp
;
3993 isl_qpolynomial
*opt
;
3997 static int opt_fn(__isl_take isl_point
*pnt
, void *user
)
3999 struct isl_opt_data
*data
= (struct isl_opt_data
*)user
;
4000 isl_qpolynomial
*val
;
4002 val
= isl_qpolynomial_eval(isl_qpolynomial_copy(data
->qp
), pnt
);
4006 } else if (data
->max
) {
4007 data
->opt
= isl_qpolynomial_max_cst(data
->opt
, val
);
4009 data
->opt
= isl_qpolynomial_min_cst(data
->opt
, val
);
4015 __isl_give isl_qpolynomial
*isl_qpolynomial_opt_on_domain(
4016 __isl_take isl_qpolynomial
*qp
, __isl_take isl_set
*set
, int max
)
4018 struct isl_opt_data data
= { NULL
, 1, NULL
, max
};
4023 if (isl_upoly_is_cst(qp
->upoly
)) {
4028 set
= fix_inactive(set
, qp
);
4031 if (isl_set_foreach_point(set
, opt_fn
, &data
) < 0)
4035 isl_space
*space
= isl_qpolynomial_get_domain_space(qp
);
4036 data
.opt
= isl_qpolynomial_zero_on_domain(space
);
4040 isl_qpolynomial_free(qp
);
4044 isl_qpolynomial_free(qp
);
4045 isl_qpolynomial_free(data
.opt
);
4049 __isl_give isl_qpolynomial
*isl_qpolynomial_morph_domain(
4050 __isl_take isl_qpolynomial
*qp
, __isl_take isl_morph
*morph
)
4055 struct isl_upoly
**subs
;
4056 isl_mat
*mat
, *diag
;
4058 qp
= isl_qpolynomial_cow(qp
);
4063 isl_assert(ctx
, isl_space_is_equal(qp
->dim
, morph
->dom
->dim
), goto error
);
4065 n_sub
= morph
->inv
->n_row
- 1;
4066 if (morph
->inv
->n_row
!= morph
->inv
->n_col
)
4067 n_sub
+= qp
->div
->n_row
;
4068 subs
= isl_calloc_array(ctx
, struct isl_upoly
*, n_sub
);
4072 for (i
= 0; 1 + i
< morph
->inv
->n_row
; ++i
)
4073 subs
[i
] = isl_upoly_from_affine(ctx
, morph
->inv
->row
[1 + i
],
4074 morph
->inv
->row
[0][0], morph
->inv
->n_col
);
4075 if (morph
->inv
->n_row
!= morph
->inv
->n_col
)
4076 for (i
= 0; i
< qp
->div
->n_row
; ++i
)
4077 subs
[morph
->inv
->n_row
- 1 + i
] =
4078 isl_upoly_var_pow(ctx
, morph
->inv
->n_col
- 1 + i
, 1);
4080 qp
->upoly
= isl_upoly_subs(qp
->upoly
, 0, n_sub
, subs
);
4082 for (i
= 0; i
< n_sub
; ++i
)
4083 isl_upoly_free(subs
[i
]);
4086 diag
= isl_mat_diag(ctx
, 1, morph
->inv
->row
[0][0]);
4087 mat
= isl_mat_diagonal(diag
, isl_mat_copy(morph
->inv
));
4088 diag
= isl_mat_diag(ctx
, qp
->div
->n_row
, morph
->inv
->row
[0][0]);
4089 mat
= isl_mat_diagonal(mat
, diag
);
4090 qp
->div
= isl_mat_product(qp
->div
, mat
);
4091 isl_space_free(qp
->dim
);
4092 qp
->dim
= isl_space_copy(morph
->ran
->dim
);
4094 if (!qp
->upoly
|| !qp
->div
|| !qp
->dim
)
4097 isl_morph_free(morph
);
4101 isl_qpolynomial_free(qp
);
4102 isl_morph_free(morph
);
4106 static int neg_entry(void **entry
, void *user
)
4108 isl_pw_qpolynomial
**pwqp
= (isl_pw_qpolynomial
**)entry
;
4110 *pwqp
= isl_pw_qpolynomial_neg(*pwqp
);
4112 return *pwqp
? 0 : -1;
4115 __isl_give isl_union_pw_qpolynomial
*isl_union_pw_qpolynomial_neg(
4116 __isl_take isl_union_pw_qpolynomial
*upwqp
)
4118 upwqp
= isl_union_pw_qpolynomial_cow(upwqp
);
4122 if (isl_hash_table_foreach(upwqp
->dim
->ctx
, &upwqp
->table
,
4123 &neg_entry
, NULL
) < 0)
4128 isl_union_pw_qpolynomial_free(upwqp
);
4132 __isl_give isl_union_pw_qpolynomial
*isl_union_pw_qpolynomial_mul(
4133 __isl_take isl_union_pw_qpolynomial
*upwqp1
,
4134 __isl_take isl_union_pw_qpolynomial
*upwqp2
)
4136 return match_bin_op(upwqp1
, upwqp2
, &isl_pw_qpolynomial_mul
);
4139 /* Reorder the columns of the given div definitions according to the
4142 static __isl_give isl_mat
*reorder_divs(__isl_take isl_mat
*div
,
4143 __isl_take isl_reordering
*r
)
4152 extra
= isl_space_dim(r
->dim
, isl_dim_all
) + div
->n_row
- r
->len
;
4153 mat
= isl_mat_alloc(div
->ctx
, div
->n_row
, div
->n_col
+ extra
);
4157 for (i
= 0; i
< div
->n_row
; ++i
) {
4158 isl_seq_cpy(mat
->row
[i
], div
->row
[i
], 2);
4159 isl_seq_clr(mat
->row
[i
] + 2, mat
->n_col
- 2);
4160 for (j
= 0; j
< r
->len
; ++j
)
4161 isl_int_set(mat
->row
[i
][2 + r
->pos
[j
]],
4162 div
->row
[i
][2 + j
]);
4165 isl_reordering_free(r
);
4169 isl_reordering_free(r
);
4174 /* Reorder the dimension of "qp" according to the given reordering.
4176 __isl_give isl_qpolynomial
*isl_qpolynomial_realign_domain(
4177 __isl_take isl_qpolynomial
*qp
, __isl_take isl_reordering
*r
)
4179 qp
= isl_qpolynomial_cow(qp
);
4183 r
= isl_reordering_extend(r
, qp
->div
->n_row
);
4187 qp
->div
= reorder_divs(qp
->div
, isl_reordering_copy(r
));
4191 qp
->upoly
= reorder(qp
->upoly
, r
->pos
);
4195 qp
= isl_qpolynomial_reset_domain_space(qp
, isl_space_copy(r
->dim
));
4197 isl_reordering_free(r
);
4200 isl_qpolynomial_free(qp
);
4201 isl_reordering_free(r
);
4205 __isl_give isl_qpolynomial
*isl_qpolynomial_align_params(
4206 __isl_take isl_qpolynomial
*qp
, __isl_take isl_space
*model
)
4211 if (!isl_space_match(qp
->dim
, isl_dim_param
, model
, isl_dim_param
)) {
4212 isl_reordering
*exp
;
4214 model
= isl_space_drop_dims(model
, isl_dim_in
,
4215 0, isl_space_dim(model
, isl_dim_in
));
4216 model
= isl_space_drop_dims(model
, isl_dim_out
,
4217 0, isl_space_dim(model
, isl_dim_out
));
4218 exp
= isl_parameter_alignment_reordering(qp
->dim
, model
);
4219 exp
= isl_reordering_extend_space(exp
,
4220 isl_qpolynomial_get_domain_space(qp
));
4221 qp
= isl_qpolynomial_realign_domain(qp
, exp
);
4224 isl_space_free(model
);
4227 isl_space_free(model
);
4228 isl_qpolynomial_free(qp
);
4232 struct isl_split_periods_data
{
4234 isl_pw_qpolynomial
*res
;
4237 /* Create a slice where the integer division "div" has the fixed value "v".
4238 * In particular, if "div" refers to floor(f/m), then create a slice
4240 * m v <= f <= m v + (m - 1)
4245 * -f + m v + (m - 1) >= 0
4247 static __isl_give isl_set
*set_div_slice(__isl_take isl_space
*dim
,
4248 __isl_keep isl_qpolynomial
*qp
, int div
, isl_int v
)
4251 isl_basic_set
*bset
= NULL
;
4257 total
= isl_space_dim(dim
, isl_dim_all
);
4258 bset
= isl_basic_set_alloc_space(isl_space_copy(dim
), 0, 0, 2);
4260 k
= isl_basic_set_alloc_inequality(bset
);
4263 isl_seq_cpy(bset
->ineq
[k
], qp
->div
->row
[div
] + 1, 1 + total
);
4264 isl_int_submul(bset
->ineq
[k
][0], v
, qp
->div
->row
[div
][0]);
4266 k
= isl_basic_set_alloc_inequality(bset
);
4269 isl_seq_neg(bset
->ineq
[k
], qp
->div
->row
[div
] + 1, 1 + total
);
4270 isl_int_addmul(bset
->ineq
[k
][0], v
, qp
->div
->row
[div
][0]);
4271 isl_int_add(bset
->ineq
[k
][0], bset
->ineq
[k
][0], qp
->div
->row
[div
][0]);
4272 isl_int_sub_ui(bset
->ineq
[k
][0], bset
->ineq
[k
][0], 1);
4274 isl_space_free(dim
);
4275 return isl_set_from_basic_set(bset
);
4277 isl_basic_set_free(bset
);
4278 isl_space_free(dim
);
4282 static int split_periods(__isl_take isl_set
*set
,
4283 __isl_take isl_qpolynomial
*qp
, void *user
);
4285 /* Create a slice of the domain "set" such that integer division "div"
4286 * has the fixed value "v" and add the results to data->res,
4287 * replacing the integer division by "v" in "qp".
4289 static int set_div(__isl_take isl_set
*set
,
4290 __isl_take isl_qpolynomial
*qp
, int div
, isl_int v
,
4291 struct isl_split_periods_data
*data
)
4296 struct isl_upoly
*cst
;
4298 slice
= set_div_slice(isl_set_get_space(set
), qp
, div
, v
);
4299 set
= isl_set_intersect(set
, slice
);
4304 total
= isl_space_dim(qp
->dim
, isl_dim_all
);
4306 for (i
= div
+ 1; i
< qp
->div
->n_row
; ++i
) {
4307 if (isl_int_is_zero(qp
->div
->row
[i
][2 + total
+ div
]))
4309 isl_int_addmul(qp
->div
->row
[i
][1],
4310 qp
->div
->row
[i
][2 + total
+ div
], v
);
4311 isl_int_set_si(qp
->div
->row
[i
][2 + total
+ div
], 0);
4314 cst
= isl_upoly_rat_cst(qp
->dim
->ctx
, v
, qp
->dim
->ctx
->one
);
4315 qp
= substitute_div(qp
, div
, cst
);
4317 return split_periods(set
, qp
, data
);
4320 isl_qpolynomial_free(qp
);
4324 /* Split the domain "set" such that integer division "div"
4325 * has a fixed value (ranging from "min" to "max") on each slice
4326 * and add the results to data->res.
4328 static int split_div(__isl_take isl_set
*set
,
4329 __isl_take isl_qpolynomial
*qp
, int div
, isl_int min
, isl_int max
,
4330 struct isl_split_periods_data
*data
)
4332 for (; isl_int_le(min
, max
); isl_int_add_ui(min
, min
, 1)) {
4333 isl_set
*set_i
= isl_set_copy(set
);
4334 isl_qpolynomial
*qp_i
= isl_qpolynomial_copy(qp
);
4336 if (set_div(set_i
, qp_i
, div
, min
, data
) < 0)
4340 isl_qpolynomial_free(qp
);
4344 isl_qpolynomial_free(qp
);
4348 /* If "qp" refers to any integer division
4349 * that can only attain "max_periods" distinct values on "set"
4350 * then split the domain along those distinct values.
4351 * Add the results (or the original if no splitting occurs)
4354 static int split_periods(__isl_take isl_set
*set
,
4355 __isl_take isl_qpolynomial
*qp
, void *user
)
4358 isl_pw_qpolynomial
*pwqp
;
4359 struct isl_split_periods_data
*data
;
4364 data
= (struct isl_split_periods_data
*)user
;
4369 if (qp
->div
->n_row
== 0) {
4370 pwqp
= isl_pw_qpolynomial_alloc(set
, qp
);
4371 data
->res
= isl_pw_qpolynomial_add_disjoint(data
->res
, pwqp
);
4377 total
= isl_space_dim(qp
->dim
, isl_dim_all
);
4378 for (i
= 0; i
< qp
->div
->n_row
; ++i
) {
4379 enum isl_lp_result lp_res
;
4381 if (isl_seq_first_non_zero(qp
->div
->row
[i
] + 2 + total
,
4382 qp
->div
->n_row
) != -1)
4385 lp_res
= isl_set_solve_lp(set
, 0, qp
->div
->row
[i
] + 1,
4386 set
->ctx
->one
, &min
, NULL
, NULL
);
4387 if (lp_res
== isl_lp_error
)
4389 if (lp_res
== isl_lp_unbounded
|| lp_res
== isl_lp_empty
)
4391 isl_int_fdiv_q(min
, min
, qp
->div
->row
[i
][0]);
4393 lp_res
= isl_set_solve_lp(set
, 1, qp
->div
->row
[i
] + 1,
4394 set
->ctx
->one
, &max
, NULL
, NULL
);
4395 if (lp_res
== isl_lp_error
)
4397 if (lp_res
== isl_lp_unbounded
|| lp_res
== isl_lp_empty
)
4399 isl_int_fdiv_q(max
, max
, qp
->div
->row
[i
][0]);
4401 isl_int_sub(max
, max
, min
);
4402 if (isl_int_cmp_si(max
, data
->max_periods
) < 0) {
4403 isl_int_add(max
, max
, min
);
4408 if (i
< qp
->div
->n_row
) {
4409 r
= split_div(set
, qp
, i
, min
, max
, data
);
4411 pwqp
= isl_pw_qpolynomial_alloc(set
, qp
);
4412 data
->res
= isl_pw_qpolynomial_add_disjoint(data
->res
, pwqp
);
4424 isl_qpolynomial_free(qp
);
4428 /* If any quasi-polynomial in pwqp refers to any integer division
4429 * that can only attain "max_periods" distinct values on its domain
4430 * then split the domain along those distinct values.
4432 __isl_give isl_pw_qpolynomial
*isl_pw_qpolynomial_split_periods(
4433 __isl_take isl_pw_qpolynomial
*pwqp
, int max_periods
)
4435 struct isl_split_periods_data data
;
4437 data
.max_periods
= max_periods
;
4438 data
.res
= isl_pw_qpolynomial_zero(isl_pw_qpolynomial_get_space(pwqp
));
4440 if (isl_pw_qpolynomial_foreach_piece(pwqp
, &split_periods
, &data
) < 0)
4443 isl_pw_qpolynomial_free(pwqp
);
4447 isl_pw_qpolynomial_free(data
.res
);
4448 isl_pw_qpolynomial_free(pwqp
);
4452 /* Construct a piecewise quasipolynomial that is constant on the given
4453 * domain. In particular, it is
4456 * infinity if cst == -1
4458 static __isl_give isl_pw_qpolynomial
*constant_on_domain(
4459 __isl_take isl_basic_set
*bset
, int cst
)
4462 isl_qpolynomial
*qp
;
4467 bset
= isl_basic_set_params(bset
);
4468 dim
= isl_basic_set_get_space(bset
);
4470 qp
= isl_qpolynomial_infty_on_domain(dim
);
4472 qp
= isl_qpolynomial_zero_on_domain(dim
);
4474 qp
= isl_qpolynomial_one_on_domain(dim
);
4475 return isl_pw_qpolynomial_alloc(isl_set_from_basic_set(bset
), qp
);
4478 /* Factor bset, call fn on each of the factors and return the product.
4480 * If no factors can be found, simply call fn on the input.
4481 * Otherwise, construct the factors based on the factorizer,
4482 * call fn on each factor and compute the product.
4484 static __isl_give isl_pw_qpolynomial
*compressed_multiplicative_call(
4485 __isl_take isl_basic_set
*bset
,
4486 __isl_give isl_pw_qpolynomial
*(*fn
)(__isl_take isl_basic_set
*bset
))
4492 isl_qpolynomial
*qp
;
4493 isl_pw_qpolynomial
*pwqp
;
4497 f
= isl_basic_set_factorizer(bset
);
4500 if (f
->n_group
== 0) {
4501 isl_factorizer_free(f
);
4505 nparam
= isl_basic_set_dim(bset
, isl_dim_param
);
4506 nvar
= isl_basic_set_dim(bset
, isl_dim_set
);
4508 dim
= isl_basic_set_get_space(bset
);
4509 dim
= isl_space_domain(dim
);
4510 set
= isl_set_universe(isl_space_copy(dim
));
4511 qp
= isl_qpolynomial_one_on_domain(dim
);
4512 pwqp
= isl_pw_qpolynomial_alloc(set
, qp
);
4514 bset
= isl_morph_basic_set(isl_morph_copy(f
->morph
), bset
);
4516 for (i
= 0, n
= 0; i
< f
->n_group
; ++i
) {
4517 isl_basic_set
*bset_i
;
4518 isl_pw_qpolynomial
*pwqp_i
;
4520 bset_i
= isl_basic_set_copy(bset
);
4521 bset_i
= isl_basic_set_drop_constraints_involving(bset_i
,
4522 nparam
+ n
+ f
->len
[i
], nvar
- n
- f
->len
[i
]);
4523 bset_i
= isl_basic_set_drop_constraints_involving(bset_i
,
4525 bset_i
= isl_basic_set_drop(bset_i
, isl_dim_set
,
4526 n
+ f
->len
[i
], nvar
- n
- f
->len
[i
]);
4527 bset_i
= isl_basic_set_drop(bset_i
, isl_dim_set
, 0, n
);
4529 pwqp_i
= fn(bset_i
);
4530 pwqp
= isl_pw_qpolynomial_mul(pwqp
, pwqp_i
);
4535 isl_basic_set_free(bset
);
4536 isl_factorizer_free(f
);
4540 isl_basic_set_free(bset
);
4544 /* Factor bset, call fn on each of the factors and return the product.
4545 * The function is assumed to evaluate to zero on empty domains,
4546 * to one on zero-dimensional domains and to infinity on unbounded domains
4547 * and will not be called explicitly on zero-dimensional or unbounded domains.
4549 * We first check for some special cases and remove all equalities.
4550 * Then we hand over control to compressed_multiplicative_call.
4552 __isl_give isl_pw_qpolynomial
*isl_basic_set_multiplicative_call(
4553 __isl_take isl_basic_set
*bset
,
4554 __isl_give isl_pw_qpolynomial
*(*fn
)(__isl_take isl_basic_set
*bset
))
4558 isl_pw_qpolynomial
*pwqp
;
4563 if (isl_basic_set_plain_is_empty(bset
))
4564 return constant_on_domain(bset
, 0);
4566 if (isl_basic_set_dim(bset
, isl_dim_set
) == 0)
4567 return constant_on_domain(bset
, 1);
4569 bounded
= isl_basic_set_is_bounded(bset
);
4573 return constant_on_domain(bset
, -1);
4575 if (bset
->n_eq
== 0)
4576 return compressed_multiplicative_call(bset
, fn
);
4578 morph
= isl_basic_set_full_compression(bset
);
4579 bset
= isl_morph_basic_set(isl_morph_copy(morph
), bset
);
4581 pwqp
= compressed_multiplicative_call(bset
, fn
);
4583 morph
= isl_morph_dom_params(morph
);
4584 morph
= isl_morph_ran_params(morph
);
4585 morph
= isl_morph_inverse(morph
);
4587 pwqp
= isl_pw_qpolynomial_morph_domain(pwqp
, morph
);
4591 isl_basic_set_free(bset
);
4595 /* Drop all floors in "qp", turning each integer division [a/m] into
4596 * a rational division a/m. If "down" is set, then the integer division
4597 * is replaced by (a-(m-1))/m instead.
4599 static __isl_give isl_qpolynomial
*qp_drop_floors(
4600 __isl_take isl_qpolynomial
*qp
, int down
)
4603 struct isl_upoly
*s
;
4607 if (qp
->div
->n_row
== 0)
4610 qp
= isl_qpolynomial_cow(qp
);
4614 for (i
= qp
->div
->n_row
- 1; i
>= 0; --i
) {
4616 isl_int_sub(qp
->div
->row
[i
][1],
4617 qp
->div
->row
[i
][1], qp
->div
->row
[i
][0]);
4618 isl_int_add_ui(qp
->div
->row
[i
][1],
4619 qp
->div
->row
[i
][1], 1);
4621 s
= isl_upoly_from_affine(qp
->dim
->ctx
, qp
->div
->row
[i
] + 1,
4622 qp
->div
->row
[i
][0], qp
->div
->n_col
- 1);
4623 qp
= substitute_div(qp
, i
, s
);
4631 /* Drop all floors in "pwqp", turning each integer division [a/m] into
4632 * a rational division a/m.
4634 static __isl_give isl_pw_qpolynomial
*pwqp_drop_floors(
4635 __isl_take isl_pw_qpolynomial
*pwqp
)
4642 if (isl_pw_qpolynomial_is_zero(pwqp
))
4645 pwqp
= isl_pw_qpolynomial_cow(pwqp
);
4649 for (i
= 0; i
< pwqp
->n
; ++i
) {
4650 pwqp
->p
[i
].qp
= qp_drop_floors(pwqp
->p
[i
].qp
, 0);
4657 isl_pw_qpolynomial_free(pwqp
);
4661 /* Adjust all the integer divisions in "qp" such that they are at least
4662 * one over the given orthant (identified by "signs"). This ensures
4663 * that they will still be non-negative even after subtracting (m-1)/m.
4665 * In particular, f is replaced by f' + v, changing f = [a/m]
4666 * to f' = [(a - m v)/m].
4667 * If the constant term k in a is smaller than m,
4668 * the constant term of v is set to floor(k/m) - 1.
4669 * For any other term, if the coefficient c and the variable x have
4670 * the same sign, then no changes are needed.
4671 * Otherwise, if the variable is positive (and c is negative),
4672 * then the coefficient of x in v is set to floor(c/m).
4673 * If the variable is negative (and c is positive),
4674 * then the coefficient of x in v is set to ceil(c/m).
4676 static __isl_give isl_qpolynomial
*make_divs_pos(__isl_take isl_qpolynomial
*qp
,
4682 struct isl_upoly
*s
;
4684 qp
= isl_qpolynomial_cow(qp
);
4687 qp
->div
= isl_mat_cow(qp
->div
);
4691 total
= isl_space_dim(qp
->dim
, isl_dim_all
);
4692 v
= isl_vec_alloc(qp
->div
->ctx
, qp
->div
->n_col
- 1);
4694 for (i
= 0; i
< qp
->div
->n_row
; ++i
) {
4695 isl_int
*row
= qp
->div
->row
[i
];
4699 if (isl_int_lt(row
[1], row
[0])) {
4700 isl_int_fdiv_q(v
->el
[0], row
[1], row
[0]);
4701 isl_int_sub_ui(v
->el
[0], v
->el
[0], 1);
4702 isl_int_submul(row
[1], row
[0], v
->el
[0]);
4704 for (j
= 0; j
< total
; ++j
) {
4705 if (isl_int_sgn(row
[2 + j
]) * signs
[j
] >= 0)
4708 isl_int_cdiv_q(v
->el
[1 + j
], row
[2 + j
], row
[0]);
4710 isl_int_fdiv_q(v
->el
[1 + j
], row
[2 + j
], row
[0]);
4711 isl_int_submul(row
[2 + j
], row
[0], v
->el
[1 + j
]);
4713 for (j
= 0; j
< i
; ++j
) {
4714 if (isl_int_sgn(row
[2 + total
+ j
]) >= 0)
4716 isl_int_fdiv_q(v
->el
[1 + total
+ j
],
4717 row
[2 + total
+ j
], row
[0]);
4718 isl_int_submul(row
[2 + total
+ j
],
4719 row
[0], v
->el
[1 + total
+ j
]);
4721 for (j
= i
+ 1; j
< qp
->div
->n_row
; ++j
) {
4722 if (isl_int_is_zero(qp
->div
->row
[j
][2 + total
+ i
]))
4724 isl_seq_combine(qp
->div
->row
[j
] + 1,
4725 qp
->div
->ctx
->one
, qp
->div
->row
[j
] + 1,
4726 qp
->div
->row
[j
][2 + total
+ i
], v
->el
, v
->size
);
4728 isl_int_set_si(v
->el
[1 + total
+ i
], 1);
4729 s
= isl_upoly_from_affine(qp
->dim
->ctx
, v
->el
,
4730 qp
->div
->ctx
->one
, v
->size
);
4731 qp
->upoly
= isl_upoly_subs(qp
->upoly
, total
+ i
, 1, &s
);
4741 isl_qpolynomial_free(qp
);
4745 struct isl_to_poly_data
{
4747 isl_pw_qpolynomial
*res
;
4748 isl_qpolynomial
*qp
;
4751 /* Appoximate data->qp by a polynomial on the orthant identified by "signs".
4752 * We first make all integer divisions positive and then split the
4753 * quasipolynomials into terms with sign data->sign (the direction
4754 * of the requested approximation) and terms with the opposite sign.
4755 * In the first set of terms, each integer division [a/m] is
4756 * overapproximated by a/m, while in the second it is underapproximated
4759 static int to_polynomial_on_orthant(__isl_take isl_set
*orthant
, int *signs
,
4762 struct isl_to_poly_data
*data
= user
;
4763 isl_pw_qpolynomial
*t
;
4764 isl_qpolynomial
*qp
, *up
, *down
;
4766 qp
= isl_qpolynomial_copy(data
->qp
);
4767 qp
= make_divs_pos(qp
, signs
);
4769 up
= isl_qpolynomial_terms_of_sign(qp
, signs
, data
->sign
);
4770 up
= qp_drop_floors(up
, 0);
4771 down
= isl_qpolynomial_terms_of_sign(qp
, signs
, -data
->sign
);
4772 down
= qp_drop_floors(down
, 1);
4774 isl_qpolynomial_free(qp
);
4775 qp
= isl_qpolynomial_add(up
, down
);
4777 t
= isl_pw_qpolynomial_alloc(orthant
, qp
);
4778 data
->res
= isl_pw_qpolynomial_add_disjoint(data
->res
, t
);
4783 /* Approximate each quasipolynomial by a polynomial. If "sign" is positive,
4784 * the polynomial will be an overapproximation. If "sign" is negative,
4785 * it will be an underapproximation. If "sign" is zero, the approximation
4786 * will lie somewhere in between.
4788 * In particular, is sign == 0, we simply drop the floors, turning
4789 * the integer divisions into rational divisions.
4790 * Otherwise, we split the domains into orthants, make all integer divisions
4791 * positive and then approximate each [a/m] by either a/m or (a-(m-1))/m,
4792 * depending on the requested sign and the sign of the term in which
4793 * the integer division appears.
4795 __isl_give isl_pw_qpolynomial
*isl_pw_qpolynomial_to_polynomial(
4796 __isl_take isl_pw_qpolynomial
*pwqp
, int sign
)
4799 struct isl_to_poly_data data
;
4802 return pwqp_drop_floors(pwqp
);
4808 data
.res
= isl_pw_qpolynomial_zero(isl_pw_qpolynomial_get_space(pwqp
));
4810 for (i
= 0; i
< pwqp
->n
; ++i
) {
4811 if (pwqp
->p
[i
].qp
->div
->n_row
== 0) {
4812 isl_pw_qpolynomial
*t
;
4813 t
= isl_pw_qpolynomial_alloc(
4814 isl_set_copy(pwqp
->p
[i
].set
),
4815 isl_qpolynomial_copy(pwqp
->p
[i
].qp
));
4816 data
.res
= isl_pw_qpolynomial_add_disjoint(data
.res
, t
);
4819 data
.qp
= pwqp
->p
[i
].qp
;
4820 if (isl_set_foreach_orthant(pwqp
->p
[i
].set
,
4821 &to_polynomial_on_orthant
, &data
) < 0)
4825 isl_pw_qpolynomial_free(pwqp
);
4829 isl_pw_qpolynomial_free(pwqp
);
4830 isl_pw_qpolynomial_free(data
.res
);
4834 static int poly_entry(void **entry
, void *user
)
4837 isl_pw_qpolynomial
**pwqp
= (isl_pw_qpolynomial
**)entry
;
4839 *pwqp
= isl_pw_qpolynomial_to_polynomial(*pwqp
, *sign
);
4841 return *pwqp
? 0 : -1;
4844 __isl_give isl_union_pw_qpolynomial
*isl_union_pw_qpolynomial_to_polynomial(
4845 __isl_take isl_union_pw_qpolynomial
*upwqp
, int sign
)
4847 upwqp
= isl_union_pw_qpolynomial_cow(upwqp
);
4851 if (isl_hash_table_foreach(upwqp
->dim
->ctx
, &upwqp
->table
,
4852 &poly_entry
, &sign
) < 0)
4857 isl_union_pw_qpolynomial_free(upwqp
);
4861 __isl_give isl_basic_map
*isl_basic_map_from_qpolynomial(
4862 __isl_take isl_qpolynomial
*qp
)
4866 isl_vec
*aff
= NULL
;
4867 isl_basic_map
*bmap
= NULL
;
4873 if (!isl_upoly_is_affine(qp
->upoly
))
4874 isl_die(qp
->dim
->ctx
, isl_error_invalid
,
4875 "input quasi-polynomial not affine", goto error
);
4876 aff
= isl_qpolynomial_extract_affine(qp
);
4879 dim
= isl_qpolynomial_get_space(qp
);
4880 pos
= 1 + isl_space_offset(dim
, isl_dim_out
);
4881 n_div
= qp
->div
->n_row
;
4882 bmap
= isl_basic_map_alloc_space(dim
, n_div
, 1, 2 * n_div
);
4884 for (i
= 0; i
< n_div
; ++i
) {
4885 k
= isl_basic_map_alloc_div(bmap
);
4888 isl_seq_cpy(bmap
->div
[k
], qp
->div
->row
[i
], qp
->div
->n_col
);
4889 isl_int_set_si(bmap
->div
[k
][qp
->div
->n_col
], 0);
4890 if (isl_basic_map_add_div_constraints(bmap
, k
) < 0)
4893 k
= isl_basic_map_alloc_equality(bmap
);
4896 isl_int_neg(bmap
->eq
[k
][pos
], aff
->el
[0]);
4897 isl_seq_cpy(bmap
->eq
[k
], aff
->el
+ 1, pos
);
4898 isl_seq_cpy(bmap
->eq
[k
] + pos
+ 1, aff
->el
+ 1 + pos
, n_div
);
4901 isl_qpolynomial_free(qp
);
4902 bmap
= isl_basic_map_finalize(bmap
);
4906 isl_qpolynomial_free(qp
);
4907 isl_basic_map_free(bmap
);